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V. M. (Nitant) Kenkre; Luca Giuggioli

References

Published online by Cambridge University Press: 14 January 2021

V. M. (Nitant) Kenkre and

Luca Giuggioli

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V. M. (Nitant) Kenkre: Affiliation:
University of New Mexico
Luca Giuggioli: Affiliation:
University of Bristol

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Type: Chapter
Information: Theory of the Spread of Epidemics and Movement Ecology of Animals
An Interdisciplinary Approach using Methodologies of Physics and Mathematics
, pp. 272 - 295

DOI: https://doi.org/10.1017/9781108882279 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2021

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References

Abbott, K. D., Ksiazek, T. G., and Mills, J. N. 1999. Long-term hantavirus persistence in rodent populations in central Arizona. Emerging Infectious Diseases, 5(1), 102.Google Scholar

Abramowitz, M., and Stegun, I. A. 1965. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover.Google Scholar

Abramson, G. 2003. Waves of Hanta. Pages 291–299 of: Kenkre, V. M., and Lindenberg, K. (eds.), AIP conference proceedings on Modern Challenges in Statistical Mechanics: Patterns, Noise, and the Interplay of Nonlinearity and Complexity, vol. 658. Melville, NY: American Institute of Physics.Google Scholar

Abramson, G., Bishop, A. R., and Kenkre, V. M. 2001. Effects of transport memory and nonlinear damping in a generalized Fisher’s equation. Physical Review E, 64(6), 066615.Google Scholar

Abramson, G., Giuggioli, L., Kenkre, V. M., Dragoo, J. W., Parmenter, R. R., Parmenter, C. A., and Yates, T. L. 2006. Diffusion and home range parameters for rodents: Peromyscus maniculatus in New Mexico. Ecological Complexity, 3, 64–70.Google Scholar

Abramson, G., Giuggioli, L., Parmenter, R. R., and Kenkre, V. M. 2013. Quasi-one-dimensional waves in rodent populations in heterogeneous habitats: a consequence of elevational gradients on spatio-temporal dynamics. Journal of Theoretical Biology, 319, 96–101.Google Scholar

Abramson, G., and Kenkre, V. M. 2002. Spatio-temporal patterns in the Hantavirus infection. Physical Review E, 66(5), 011912.CrossRef Google Scholar

Abramson, G., Kenkre, V. M., and Bishop, A. R. 2002. Analytic solutions for nonlinear waves in coupled reacting systems. Physica A: Statistical Mechanics and Its Applications, 305(3–4), 427–436.Google Scholar

Abramson, G., Kenkre, V. M., Yates, T. L., and Parmenter, R. R. 2003. Traveling waves of infection in the Hantavirus epidemics. Ecological Complexity, 65, 519–534.Google Scholar

Abramson, G., and Wio, H. S. 1995. Time behaviour for diffusion in the presence of static imperfect traps. Chaos, Solitons & Fractals, 6, 1–5.Google Scholar

Acebrón, J. A., Bonilla, L. L., Vicente, C. J. P., Ritort, F., and Spigler, R. 2005. The Kuramoto model: a simple paradigm for synchronization phenomena. Reviews of Modern Physics, 77(1), 137.Google Scholar

Adams, E. S. 2001. Approaches to the study of territory size and shape. Annual Review of Ecology and Systematics, 32, 277–303.Google Scholar

Aguirre, M. A., Abramson, G., Bishop, A. R., and Kenkre, V. M. 2002. Simulations in the mathematical modeling of the spread of the Hantavirus. Physical Review E, 66, 041908.Google Scholar

Alberts, A. C. 1992. Constraints on the design of chemical communication systems in terrestrial vertebrates. American Naturalist, 139, S62–S89.Google Scholar

Aldana, M., Dossetti, V., Huepe, C., Kenkre, V. M., and Larralde, H. 2007. Phase transitions in systems of self-propelled agents and related network models. Physical Review Letters, 98, 095702.Google Scholar

Aldana, M., and Huepe, C. 2003. Phase transitions in self-driven many-particle systems and related non-equilibrium models: a network approach. Journal of Statistical Physics, 112(1–2), 135–153.Google Scholar

Allee, W. C. 1938. The Social Life of Animals. New York: W.W. Norton &Co.Google Scholar

Aoki, I. 1982. A simulation study on the schooling mechanism in fish. Bulletin of the Japanese Society of Scientific Fisheries, 48.Google Scholar

Aranson, I. S., and Tsimring, L. S. 2006. Patterns and collective behavior in granular media: theoretical concepts. Reviews of Modern Physics, 78(2), 641.Google Scholar

Aronson, D. G., and Weinberger, H. F. 1975. Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation. Pages 5–49 of: Byrne, G. (ed.), Partial Differential Equations and Related Topics. Berlin: Springer.Google Scholar

Aronson, D. G., and Weinberger, H. F. 1978. Multidimensional nonlinear diffusion arising in population genetics. Advances in Mathematics, 30(1), 33–76.Google Scholar

Asakura, S., and Oosawa, F. 1958. Interaction between particles suspended in solutions of macromolecules. Journal of Polymer Science, 33(126), 183–192.Google Scholar

Astwood, A. M. 2012. Transport Studies of Some Microscopic and Macroscopic Systems. Ph thesis, University of New Mexico, Albuquerque, NM.Google Scholar

Astwood, A., and Kenkre, V. M. 2020. Simple Smoluchowski models for flocking. University of New Mexico preprint.Google Scholar

Attanasi, A., Cavagna, A., Del Castello, L., Giardina, I., Grigera, T. S., Jelić, A., Melillo, S., Parisi, L., Pohl, O., Shen, E., and Viale, M. 2014. Information transfer and behavioural inertia in starling flocks. Nature Physics, 10(9), 691–696.Google Scholar

Baglietto, G., and Albano, E. V. 2009. Nature of the order-disorder transition in the Vicsek model for the collective motion of self-propelled particles. Physical Review E, 80(5), 050103.CrossRef Google Scholar PubMed

Bailey, N. T. J. 1975. The Mathematical Theory of Infectious Diseases and Its Applications. London: Charles Griffin & Co.Google Scholar

Bajec, I. L., and Heppner, F. H. 2009. Organized flight in birds. Animal Behaviour, 78(4), 777–789.Google Scholar

Balescu, R. 1975. Equilibrium and Nonequilibrium Statistical Mechanics. New York: John Wiley & Sons.Google Scholar

Ball, P. 1999. The Self-Made Tapestry: Pattern Formation in Nature. Oxford, UK: Oxford University Press.Google Scholar

Ballard, M., Kenkre, V. M., and Kuperman, M. N. 2004. Periodically varying externally imposed environmental effects on population dynamics. Physical Review E, 70(3), 031912.CrossRef Google Scholar PubMed

Ballerini, M., Cabibbo, N., Candelier, R., Cavagna, A., Cisbani, E., Giardina, I., Lecomte, V., Orlandi, A., Parisi, G., Procaccini, A., Viale, M., and Zdravkovic, V. 2008. Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study. Proceedings of the National Academy of Sciences USA, 105(4), 1232–1237.Google Scholar

Banavar, J. R., Damuth, J., Maritan, A., and Rinaldo, A. 2002. Supply–demand balance and metabolic scaling. Proceedings of the National Academy of Sciences USA, 99(16), 10506–10509.Google Scholar

Barabási, A.-L. 2002. Linked: The New Science of Networks. Cambridge, UK: Perseus.Google Scholar

Barabási, A.-L., and Stanley, H. E. 1995. Fractal Concepts in Surface Growth. Cambridge, UK: Cambridge University Press.Google Scholar

Barkai, E., Metzler, R., and Klafter, J. 2000. From continuous time random walks to the fractional Fokker–Planck equation. Physical Review E, 61(1), 132.Google Scholar

Bartumeus, F., da Luz, M. G. E., Viswanathan, G. M., and Catalan, J. 2005. Animal search strategies: a quantitative random-walk analysis. Ecology, 86(11), 3078–3087.Google Scholar

Bartumeus, F., Giuggioli, L., Louzao, M., Bretagnolle, V., Oro, D., and Levin, S. A. 2010. Fishery discards impact on seabird movement patterns at regional scales. Current Biology, 20, 215–222.Google Scholar

Bazazi, S., Buhl, J., Hale, J. J., Anstey, M. L., Sword, G. A., Simpson, S. J., and Couzin, I. D. 2008. Collective motion and cannibalism in locust migratory bands. Current Biology, 18(10), 735–739.Google Scholar

Bechinger, C., Rudhardt, D., Leiderer, P., Roth, R., and Dietrich, S. 1999. Understanding depletion forces beyond entropy. Physical Review Letters, 83(19), 3960.Google Scholar

Be’er, A., and Ariel, G. 2019. A statistical physics view of swarming bacteria. Movement Ecology, 7(9).Google Scholar

Bel, G., and Barkai, E. 2005. Weak ergodicity breaking in the continuous-time random walk. Physical Review Letters, 94(24), 240602.Google Scholar

Ben-Jacob, E., Cohen, I., and Levine, H. 2000. Cooperative self-organization of microorganisms. Advances in Physics, 49(4), 395–554.Google Scholar

Benhamou, S. 2007. How many animals really do the Lévy walk? Ecology, 88(8), 1962–1969.Google Scholar

Benhamou, S., and Cornelis, D. 2010. Incorporating movement behavior and barriers to improve kernel home range space use estimates. Journal of Wildlife Management, 74, 1353–1360.Google Scholar

Berg, H. C. 1993. Random Walks in Biology. Princeton, NJ: Princeton University Press.Google Scholar

Berg, H. C. 2000. Motile behavior of bacteria. Physics Today, 53(1), 24–29.Google Scholar

Berthier, L., Jacquin, H., and Zamponi, F. 2011. Microscopic theory of the jamming transition of harmonic spheres. Physical Review E, 84(5), 051103.CrossRef Google Scholar PubMed

Bertin, E., Droz, M., and Grégoire, G. 2006. Boltzmann and hydrodynamic description for self-propelled particles. Physical Review E, 74(2), 022101.Google Scholar

Bertin, E., Droz, M., and Grégoire, G. 2009. Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis. Journal of Physics A: Mathematical and Theoretical, 42(44), 445001.Google Scholar

Biagini, F., Hu, Y., Øksendal, B., and Zhang, T. 2010. Stochastic Calculus for Fractional Brownian Motion and Applications. London: Springer.Google Scholar

Bialek, W., Cavagna, A., Giardina, I., Mora, T., Pohl, O., Silvestri, E., Viale, M., and Walczak, A. M. 2014. Social interactions dominate speed control in poising natural flocks near criticality. Proceedings of the National Academy of Sciences USA, 111(20), 7212–7217.Google Scholar

Binder, K., and Kob, W. 2011. Glassy Materials and Disordered Solids: An Introduction to Their Statistical Mechanics. Second ed. Singapore: World Scientific.CrossRef Google Scholar

Bolker, B. M. 2008. Ecological models and data in R. Princeton, NJ: Princeton University Press.Google Scholar

Boltzmann, L. 1872. Weitere studien über das wärme gleichgewicht unter gasmoläkülen. Sitzungsberichte der Akademie der Wissenschaften in Wien, 66, 275–370.Google Scholar

Börger, L., Dalziel, B. D., and Fryxell, J. M. 2008. Are there general mechanisms of animal home range behaviour? A review and prospects for future research. Ecology Letters, 11, 637–650.Google Scholar

Botten, J., Mirowsky, K., Ye, C., Gottlieb, K., Saavedra, M., Ponce, L., and Hjelle, B. 2002. Shedding and intracage transmission of Sin Nombre hantavirus in the deer mouse (Peromyscus maniculatus) model. Journal of Virology, 76(15), 7587–7594.Google Scholar

Bovet, P., and Benhamou, S. 1988. Spatial analysis of animals’ movements using a correlated random walk model. Journal of Theoretical Biology, 131(4), 419–433.CrossRef Google Scholar

Bowen, W., and McTaggart Cowan, I. 1980. Scent marking in coyotes. Canadian Journal of Zoology, 58(4), 473–480.CrossRef Google Scholar

Bowman, F. 1953. Introduction to Elliptic Functions: With Applications. New York: Dover Publications.Google Scholar

Boyer, D., and Solis-Salas, C. 2014. Random walks with preferential relocations to places visited in the past and their application to biology. Physical Review Letters, 112, 240601.Google Scholar

Boys, C. V. 1959. Soap Bubbles, Their Colours and the Forces Which Mold Them. New York: Courier Corporation.Google Scholar

Brauer, F., and Castillo-Chavez, C. 2012. Mathematical Models in Population Biology and Epidemiology. 2nd ed. New York: Springer.Google Scholar

Brazhkin, V. V., Fomin, Yu, D., Lyapin, A. G., Ryzhov, V. N., Tsiok, E. N., and Trachenko, K. 2013. “Liquid-gas” transition in the supercritical region: fundamental changes in the particle dynamics. Physical Review Letters, 111(13), 145901 1–5.Google Scholar

Brenner, M. P., Levitov, L. S., and Budrene, E. O. 1998. Physical mechanisms for chemotactic pattern formation by bacteria. Biophysical Journal, 74(4), 1677–1693.Google Scholar

Brown, J. L., and Orians, G. H. 1970. Spacing patterns in mobile animals. Annual Review of Ecology and Systematics, 1, 239–262.Google Scholar

Buhl, J., Sumpter, D. J. T., Couzin, I. D., Hale, J. J., Despland, E., Miller, E. R., and Simpson, S. J. 2006. From disorder to order in marching locusts. Science, 312, 1402–1406.Google Scholar

Burt, W. H. 1943. Territoriality and home range concepts as applied to mammals. Journal of Mammalogy, 24, 346–352.Google Scholar

Cagnacci, F., Boitani, L., Powell, R. A., and Boyce, M. S. 2010. Animal ecology meets GPS-based radiotelemetry: a perfect storm of opportunities and challenges. Philosophical Transactions of the Royal Society B, 365, 2157–2162.Google Scholar

Calisher, C. H., Sweeney, W., Mills, J. N., and Beaty, B. J. 1999. Natural history of Sin Nombre virus in western Colorado. Emerging Infectious Diseases, 5(1), 126.Google Scholar

Camazine, S., Deneubourg, J. L., Franks, N. R., Sneyd, J., Theraulaz, G., and Bonabeau, E. 2001. Self-Organization in Biological Systems. Princeton, NJ: Princeton University Press.Google Scholar

Camelo-Neto, G., Silva, A. T. C., Giuggioli, L., and Kenkre, V. M. 2008. Effect of predators of juvenile rodents on the spread of the Hantavirus epidemic. Bulletin of Mathematical Biology, 70(1), 179–188.Google Scholar

Candia, J., Parris, P. E., and Kenkre, V. M. 2007. Transport properties of random walks on scale-free/regular-lattice hybrid networks. Journal of Statistical Physics, 129(2), 323–333.Google Scholar

Canosa, J. 1973. On a nonlinear diffusion equation describing population growth. IBM Journal of Research and Development, 17(4), 307–313.Google Scholar

Cantrell, R. S., and Cosner, C. 2003. Spatial Ecology via Reaction-Diffusion Equations. Chichester, UK: Wiley & Sons.Google Scholar

Cao, P.-L. 1994. Computer experiments for surface diffusion: the real time in Monte Carlo simulation. Physical Review Letters, 73(19), 2595.Google Scholar

Carpenter, C. R. 1934. A field study of the behavior and social relations of howling monkeys (Alouatta palliata). Comparative Psychology Monograph, 10(2), 1–168.Google Scholar

Carslaw, H. S., and Jaeger, J. C. 1959. Conduction of Heat in Solids. Oxford, UK: Clarendon Press.Google Scholar

Cavagna, A., Del Castello, L., Giardina, I., Grigera, T., Jelic, A., Melillo, S., Mora, T., Parisi, L., Silvestri, E., Viale, M., and Walczak, A. M. 2015. Flocking and turning: a new model for self-organized collective motion. Journal of Statistical Physics, 158(3), 601–627.Google Scholar

Cavagna, A., Giardina, I., and Grigera, T. S. 2018. The physics of flocking: correlation as a compass from experiments to theory. Physics Reports, 728, 1–62.Google Scholar

Chaikin, P. M., Lubensky, T. C., and Witten, T. A. 1995. Principles of Condensed Matter Physics. Vol. 10. Cambridge, UK: Cambridge University Press.Google Scholar

Chandrasekhar, S. 1943. Stochastic problems in physics and astronomy. Reviews of Modern Physics, 15, 1–89.Google Scholar

Chase, M. 2016. Memory Effects in Brownian Motion, Random Walks under Confining Potentials, and Relaxation of Quantum Systems. PhD thesis, University of New Mexico, Albuquerque, NM.Google Scholar

Chase, M., Spendier, K., and Kenkre, V. M. 2016. Analysis of confined random walkers with applications to processes occurring in molecular aggregates and immunological systems. Journal of Physical Chemistry B, 120(12), 3072–3080.CrossRef Google Scholar PubMed

Chaté, H., Ginelli, F., Grégoire, G., and Raynaud, F. 2008. Collective motion of self-propelled particles interacting without cohesion. Physical Review E, 77(4), 046113.Google Scholar

Chepizhko, A. A., and Kulinskii, V. L. 2009. The kinetic regime of the Vicsek model. Pages 25–33 of: AIP Conference Proceedings on Statistical Physics: Modern Trends and Applications, vol. 1198. Melville, NY: American Institute of Physics.Google Scholar

Chepizhko, A. A., and Kulinskii, V. L. 2010. On the relation between Vicsek and Kuramoto models of spontaneous synchronization. Physica A: Statistical Mechanics and Its Applications, 389(23), 5347–5352.Google Scholar

Chepizhko, A. A., and Kulinskii, V. L. 2014. The hydrodynamic description for the system of self-propelled particles: ideal Viscek fluid. Physica A: Statistical Mechanics and Its Applications, 415, 493–502.Google Scholar

Childs, J. E., Ksiazek, T. G., Spiropoulou, C. F., Krebs, J. W., Morzunov, S., Maupin, G. O., Gage, K. L., Rollin, P. E., Sarisky, J., Enscore, R. E., Frey, J. K., Peters, C. J., and Nichol, S. T. 1994. Serologic and genetic identification of Peromyscus maniculatus as the primary rodent reservoir for a new hantavirus in the southwestern United States. Journal of Infectious Diseases, 169(6), 1271–1280.CrossRef Google Scholar PubMed

Christiansen, P. L., and Scott, A. C. 1990. Davydov’s Soliton Revisited: Self-Trapping of Vibrational Energy in Protein. Vol. 243. New York: Plenum Press.Google Scholar

Chupeau, M., Bénichou, O., and Voituriez, R. 2015. Cover times of random searches. Nature Physics, 11(10), 844.Google Scholar

Clayton, R. K. 1980. Photosynthesis: Physical Mechanisms and Chemical Patterns. Cambridge, UK: Cambridge University Press.Google Scholar

Clerc, M. G., Escaff, D., and Kenkre, V. M. 2005. Patterns and localized structures in population dynamics. Physical Review E, 72(5), 056217.Google Scholar

Clerc, M. G., Escaff, D., and Kenkre, V. M. 2010. Analytical studies of fronts, colonies, and patterns: combination of the Allee effect and nonlocal competition interactions. Physical Review E, 82(3), 036210.Google Scholar

Codling, E. A., Planck, M. J., and Benhamou, S. 2008. Random walk models in biology. Journal of the Royal Society Interface, 95(5), 813–834.Google Scholar

Cooke, S. J., Hinch, S. G., Wikelski, M., Andrews, R. D., Kuchel, L. J., Wolcott, T. G., and Butler, P. J. 2004. Biotelemetry: a mechanistic approach to ecology. Trends in Ecology and Evolution, 19, 334–343.Google Scholar

Courchamp, F., Berec, L., and Gascoigne, J. 2008. Allee Effects in Ecology and Conservation. New York: Oxford University Press.Google Scholar

Courchamp, F., Clutton-Brock, T., and Grenfell, B. 1999. Inverse density dependence and the Allee effect. Trends in Ecology and Evolution, 14(10), 405–410.Google Scholar

Couzin, I. D., and Franks, N. R. 2003. Self-organized lane formation and optimized traffic flow in army ants. Proceedings of the Royal Society of London. Series B: Biological Sciences, 270(1511), 139–146.Google Scholar

Couzin, I. D., Krause, J., Franks, N. R., and Levin, S. A. 2005. Effective leadership and decision-making in animal groups on the move. Journal of Theoretical Biology, 218, 1–11.Google Scholar

Couzin, I. D., Krause, J., James, R., Ruxton, G. D., and Franks, N. R. 2002. Collective memory and spatial sorting in animal groups. Nature, 433, 513–516.Google Scholar

Cross, M. C., and Hohenberg, P. C. 1993. Pattern formation outside of equilibrium. Reviews of Modern Physics, 65(3), 851.Google Scholar

Czirók, A., Ben-Jacob, E., Cohen, I., and Vicsek, T. 1996. Formation of complex bacterial colonies via self-generated vortices. Physical Review E, 54(2), 1791.CrossRef Google Scholar PubMed

Dahmen, K. A., Nelson, D. R., and Shnerb, N. M. 2000. Life and death near a windy oasis. Journal of Mathematical Biology, 41(1), 1–23.Google Scholar

Davies, N. B., and Houston, A. I. 1984. Territory economics. Pages 148–169 of: Krebs, J. R., and Davies, N. B. (eds.), Behavioural Ecology: An Evolutionary Approach, 2nd ed. Oxford, UK: Blackwell Science.Google Scholar

Dawnkaski, E. J., Srivastava, D., and Garrison, B. J. 1995. Time dependent Monte Carlo simulations of H reactions on the diamond {001}(2×1) surface under chemical vapor deposition conditions. Journal of Chemical Physics, 102(23), 9401–9411.Google Scholar

DeAngelis, D. L., and Gross, L. J. 2018. Individual-Based Models and Approaches in Ecology: Populations, Communities and Ecosystems. Boca Raton, FL: CRC Press.Google Scholar

DeWit, R. 1971. Relation between dislocations and disclinations. Journal of Applied Physics, 42(9), 3304–3308.Google Scholar

Doncaster, C. P., and Woodroffe, R. 1993. Den site can determine shape and size of badger territories: implications for group-living. Oikos, 66, 88–93.CrossRef Google Scholar

Dossetti, V., and Sevilla, F. J. 2015. Emergence of collective motion in a model of interacting brownian particles. Physical Review Letters, 115(5), 058301.Google Scholar

Downs, J. A., Horner, M. W., and Tucker, A. D. 2011. Time-geographic density estimation for home range analysis. Annals GIS, 17(3), 163–171.Google Scholar

Dresden, M. 1961. Recent developments in the quantum theory of transport and galvano-magnetic phenomena. Reviews of Modern Physics, 33(2), 265.Google Scholar

Durrett, R., and Levin, S. A. 1994. The importance of being discrete (and spatial). Theoretical Population Biology, 46, 363–394.Google Scholar

Ebeling, W., and Schimansky-Geier, L. 2008. Swarm dynamics, attractors and bifurcations of active Brownian motion. European Physical Journal Special Topics, 157(1), 17–31.CrossRef Google Scholar

Ebert, U., and van Saarloos, W. 2000. Front propagation into unstable states: universal algebraic convergence towards uniformly translating pulled fronts. Physica D: Nonlinear Phenomena, 146(1–4), 1–99.Google Scholar

Edwards, A. M. 2011. Overturning conclusions of Lévy flight movement patterns by fishing boats and foraging animals. Ecology, 92(6), 1247–1257.Google Scholar

Ehrenfest, P., and Ehrenfest, T. 1959. The Conceptual Foundations of the Statistical Approach in Mechanics. Ithaca, NY: Cornell University Press.Google Scholar

Engel, M., Anderson, J. A., Glotzer, S. C., Isobe, M., Bernard, E. P., and Krauth, W. 2013. Hard-disk equation of state: first-order liquid-hexatic transition in two dimensions with three simulation methods. Physical Review E, 87, 042134.Google Scholar

Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F. G. 1953. Higher Transcendental Functions. New York: McGraw-Hill.Google Scholar

Erdmann, U., Ebeling, W., and Mikhailov, A. S. 2005. Noise-induced transition from translational to rotational motion of swarms. Physical Review E, 71(5), 051904.Google Scholar

Ernest, S. K. M., Brown, J. H., and Parmenter, R. R. 2000. Rodents, plants, and precipitation: spatial and temporal dynamics of consumers and resources. Oikos, 88(3), 470–482.Google Scholar

Escudero, C., Buceta, J., de La Rubia, F. J., and Lindenberg, K. 2004. Extinction in population dynamics. Physical Review E, 69(2), 021908.Google Scholar

Falcón-Cortés, A., Boyer, D., Giuggioli, L., and Majumdar, S. N. 2017. Localization transition induced by learning in random searches. Physical Review Letters, 119(14), 140603.Google Scholar

Farrell, F. D. C., Marchetti, M. C., Marenduzzo, D., and Tailleur, J. 2012. Pattern formation in self-propelled particles with density-dependent motility. Physical Review Letters, 108(24), 248101.Google Scholar

Fedotov, S. 2001. Front propagation into an unstable state of reaction-transport systems. Physical Review Letters, 86(5), 926.Google Scholar

Fermi, L. 2014. Atoms in the Family: My Life with Enrico Fermi. Chicago: University of Chicago Press.Google Scholar

Feynman, R. P., Leighton, R. B., and Sands, M. 2011. The Feynman Lectures on Physics, Vol. II: The New Millennium Edition: Mainly Electromagnetism and Matter. New York: Basic Books.Google Scholar

Fisher, R. A. 1937. The wave of advance of advantageous genes. Annals of Eugenics, 7(4), 355–369.Google Scholar

Förster, T. 1948. Intermolecular energy migration and fluorescence. Annalen der Physik (Leipzig), 2, 55–75.Google Scholar

Fuentes, M. A., Kuperman, M. N., and Kenkre, V. M. 2003. Nonlocal interaction effects on pattern formation in population dynamics. Physical Review Letters, 91(15), 158104.Google Scholar

Fuentes, M. A., Kuperman, M. N., and Kenkre, V. M. 2004. Analytical considerations in the study of spatial patterns arising from nonlocal interaction effects. Journal of Physical Chemistry B, 108(29), 10505–10508.Google Scholar

Gautrais, J., Ginelli, F., Fournier, R., Blanco, S., Soria, M., Chaté, H., and Theraulaz, G. 2012. Deciphering interactions in moving animal groups. PLoS Computational Biology, 8(9), e1002678.Google Scholar

Gibbs, J. W. 1902. Elementary Principles in Statistical Mechanics: Developed with Especial Reference to the Rational Foundation of Thermodynamics. New York: Scribner & Sons.Google Scholar

Giuggioli, L. 2020. Exact spatio-temporal dynamics of confined lattice random walks in arbitrary dimensions: a century after Smoluchowski and Pólya. Physical Review X, 10(2), 021045.Google Scholar

Giuggioli, L., Abramson, G., Kenkre, V. M., Parmenter, R. R., and Yates, T. L. 2006. Theory of home range estimation from displacement measurements of animal populations. Journal of Theoretical Biology, 240, 126–135.Google Scholar

Giuggioli, L., Abramson, G., Kenkre, V. M., Suzán, G., Marcé, E., and Yates, T. L. 2005. Diffusion and home range parameters from rodent population measurements in Panama. Bulletin of Mathematical Biology, 67(5), 1135–1149.Google Scholar

Giuggioli, L., Arye, I., Heiblum Robles, A., and Kaminka, G. A. 2018. From ants to birds: a novel bio-inspired approach to online area coverage. Pages 31–43 of: Distributed Autonomous Robotic Systems. Berlin: Springer.Google Scholar

Giuggioli, L., and Bartumeus, F. 2010. Animal movement, search strategies and behavioural ecology: a cross-disciplinary way forward. Journal of Animal Ecology, 79, 906–909.Google Scholar

Giuggioli, L., and Bartumeus, F. 2012. Linking animal movement to site fidelity. Journal of Mathematical Biology, 64(4), 647–656.Google Scholar

Giuggioli, L., Kalay, Z., and Kenkre, V. M. 2008. Study of transients in the propagation of nonlinear waves in some reaction diffusion systems. The European Physical Journal B, 62(3), 341.Google Scholar

Giuggioli, L., and Kenkre, V. M. 2003. Analytic solutions of a nonlinear convective equation in population dynamics. Physica D: Nonlinear Phenomena, 183(3–4), 245–259.CrossRef Google Scholar

Giuggioli, L., and Kenkre, V. M. 2014. Consequences of animal interactions on their dynamics: emergence of home ranges and territoriality. Movement Ecology, 2(20).Google Scholar

Giuggioli, L., McKetterick, T. J., and Holderied, M. 2015. Delayed response and biosonar perception explain movement coordination in trawling bats. PLoS Computational Biology, 11(3), e1004089.Google Scholar

Giuggioli, L., Potts, J. R., and Harris, S. 2011a. Animal interactions and the emergence of territoriality. PLoS Computational Biology, 7(3), e1002008.Google Scholar

Giuggioli, L., Potts, J. R., and Harris, S. 2011b. Brownian walkers within subdiffusing territorial boundaries. Physical Review E, 83, 061138.Google Scholar

Giuggioli, L., Potts, J. R., and Harris, S. 2012. Predicting oscillatory dynamics in the movement of territorial animals. Journal of the Royal Society Interface, 9(72), 1529–1543.Google Scholar

Giuggioli, L., Potts, J. R., Rubenstein, D. I., and Levin, S. A. 2013. Stigmergy, collective actions, and animal social spacing. Proceedings of the National Academy of Sciences USA, 110(42), 16904–16909.Google Scholar

Giuggioli, L., Sevilla, F. J., and Kenkre, V. M. 2009. A generalised master equation approach to modelling anomalous transport in animal movement. Journal of Physics A: Mathematical and Theoretical, 42, 434004.Google Scholar

Giuggioli, L., Viswanathan, G. M., Kenkre, V. M., Parmenter, R. R., and Yates, T. L. 2007. Effects of finite probing windows on the interpretation of the multifractal properties of random walks. Europhysics Letters, 77, 4004.Google Scholar

Glass, G. E., Cheek, J. E., Patz, J. A., Shields, T. M., Doyle, T. J., Thoroughman, D. A., Hunt, D. K., Enscore, R. E., Gage, K. L., Irland, C., Peters, C. J., and Bryan, R. 2000. Using remotely sensed data to identify areas at risk for hantavirus pulmonary syndrome. Emerging Infectious Diseases, 6(3), 238.Google Scholar

Glass, G. E., Shields, T. M., Parmenter, R. R., Goade, D., Mills, J. N., Cheek, J., Cook, J., and Yates, T. L. 2006. Predicted Hantavirus risk in 2006 for the southwestern United States. Occasional Papers, Museum of Texas Tech University, 255, 1–16.Google Scholar

Glass, G. E., Yates, T. L., Fine, J. B., Shields, T. M., Kendall, J. B., Hope, A. G., Parmenter, C. A., Peters, C. J., Ksiazek, T. G., Li, C.-S., Patz, J. A., and Mills, J. N. 2002. Satellite imagery characterizes local animal reservoir populations of Sin Nombre virus in the southwestern United States. Proceedings of the National Academy of Sciences USA, 99(26), 16817–16822.Google Scholar

Glauber, R. J. 1963. Time-dependent statistics of the Ising model. Journal of Mathematical Physics, 4(2), 294–307.Google Scholar

Goodenough, A. E., Little, N., Carpenter, W. S., and Hart, A. G. 2017. Birds of a feather flock together: insights into starling murmuration behaviour revealed using citizen science. PLoS ONE, 12(6).Google Scholar

Gordon, D. M. 1997. The population consequences of territorial behavior. Trends in Ecology and Evolution, 12, 63–66.Google Scholar

Gorenflo, R., Luchko, Y., and Mainardi, F. 1999. Analytical properties and applications of the Wright function. Fractional Calculus and Applied Analysis, 2, 383–414.Google Scholar

Gorenflo, R., Mainardi, F., Moretti, D., Pagnini, G., and Paradisi, P. 2002. Discrete random walk models for space–time fractional diffusion. Chemical Physics, 284(1–2), 521–541.Google Scholar

Gosling, L. M., and Roberts, S. C. 2001. Scent-marking by male mammals: cheat-proof signals to competitors and mates. Advances in the Study of Behavior, 30, 169–217.Google Scholar

Grassé, P.-P. 1959. La reconstruction du nid et les coordinations interindividuelles chez Bellicositermes natalensis et Cubitermes sp. La théorie de la stigmergie: essai d’nterprétation du comportement des termites constructeurs. Insectes Sociaux, 6(1), 41–80.Google Scholar

Grégoire, G., and Chaté, H. 2004. Onset of collective and cohesive motion. Physical Review Letters, 92(2), 025702.Google Scholar

Grigolini, P. 2006. The continuous-time random walk versus the generalized master equation. Pages 357–474 of: Fractals, Diffusion, and Relaxation in Disordered Complex Systems: Advances in Chemical Physics, Part A, vol. 133. Hoboken, NJ: John Wiley & Sons.Google Scholar

Grimm, V., and Railsback, S. F. 2005. Individual-Based Modeling and Ecology. Princeton, NJ: Princeton University Press.Google Scholar

Grossman, D., Aranson, I. S., and Jacob, E. B. 2008. Emergence of agent swarm migration and vortex formation through inelastic collisions. New Journal of Physics, 10(2), 023036.Google Scholar

Grossmann, R., Schimansky-Geier, L., and Romanczuk, P. 2012. Active Brownian particles with velocity-alignment and active fluctuations. New Journal of Physics, 14(7), 073033.Google Scholar

Grünbaum, D., and Okubo, A. 1994. Modelling social animal aggregations. Pages 296–325 of: Frontiers in Mathematical Biology, vol. 100 Lecture Notes in Biomathematics. Berlin: Springer.Google Scholar

Gueron, S., and Levin, S. A. 1993. Self-organization of front patterns in large wildebeest herds. Journal of Theoretical Biology, 165(4), 541–552.Google Scholar

Gueron, S., Levin, S. A., and Rubenstein, D. I. 1996. The dynamics of herds: from individuals to aggregations. Journal of Theoretical Biology, 182(1), 85–98.Google Scholar

Haggett, P. 2000. The Geographical Structure of Epidemics. Oxford, UK: Oxford University Press.Google Scholar

Haining, R. P. 2003. Spatial Data Analysis: Theory and Practice. Cambridge, UK: Cambridge University Press.Google Scholar

Halperin, B. I., and Nelson, D. R. 1978. Theory of two-dimensional melting. Physical Review Letters, 41(2), 121–124.Google Scholar

Han, Y., Ha, N. Y., Alsayed, A. M., and Yodh, A. G. 2008. Melting of two-dimensional tunable-diameter colloidal crystals. Physical Review E, 77(4), 041406.Google Scholar

Hanski, I. 1999. Metapopulation Ecology. Oxford, UK: Oxford University Press.Google Scholar

Harris, W. F. 1977. Disclinations. Scientific American, 237(6), 130–145.Google Scholar

Harrison, R. L. 1992. Toward a theory of inter-refuge corridor design. Conservation Biology, 6(2), 293–295.Google Scholar

Heiblum Robles, A., and Giuggioli, L. 2018. Phase transitions in stigmergic territorial systems. Physical Review E, 98(4), 042115.Google Scholar

Helbing, D., Farkas, I., and Vicsek, T. 2000. Simulating dynamical features of escape panic. Nature, 407(6803), 487–490.Google Scholar

Hemenger, R. P., Lakatos-Lindenberg, K., and Pearlstein, R. M. 1974 . Impurity quenching of molecular excitons. III. Partially coherent excitons in linear chains. Journal of Chemical Physics, 60(8), 3271–3277.Google Scholar

Herbert-Read, J. E., Perna, A., Mann, R. P., Schaerf, T. M., Sumpter, D. J. T., and Ward, A. J. W. 2011. Inferring the rules of interaction of shoaling fish. Proceedings of the National Academy of Sciences USA, 108, 18726–18731.Google Scholar

Hilborn, R., and Mangel, M. 1997. The Ecological Detective: Confronting Models with Data. Vol. 28. Princeton, NJ: Princeton University Press.Google Scholar

Hilfer, R., and Anton, L. 1995. Fractional master equations and fractal time random walks. Physical Review E, 51, R848–R851.Google Scholar

Hinde, R. A. 1956. The biological significance of the territory of birds. Ibis, 98, 340–369.Google Scholar

Holland, O., and Melhuish, C. 1999. Stigmergy, self-organisation and sorting in collective robotics. Artificial Life, 5(2), 173–202.Google Scholar

Holstein, T. 1959a. Studies of polaron motion: Part I. The molecular-crystal model. Annals of Physics, 8(3), 325–342.Google Scholar

Holstein, T. 1959b. Studies of polaron motion: Part II. The “small” polaron. Annals of Physics, 8(3), 343–389.Google Scholar

Hughes, B. D. 1995. Random Walks and Random Environments: Random Walks. Vol. 1. Oxford, UK: Clarendon Press.Google Scholar

Hughes, B. D., Shlesinger, M. F., and Montroll, E. W. 1981. Random walks with self-similar clusters. Proceedings of the National Academy of Sciences USA, 78(6), 3287–3291.Google Scholar

Hurst, H. E., Black, R. P., and Simaika, Y. M. 1965. Long-Term Storage: An Experimental Study. London: Constable.Google Scholar

Huth, A., and Wissel, C. 1992. The simulation of the movement of fish schools. Journal of Theoretical Biology, 156(3), 365–385.Google Scholar

Hyman, J., Hughes, M., Searcy, W. A., and Nowicki, S. 2004. Individual variation in the strength of territory defense in male song sparrows: correlates of age, territory tenure, and neighbor aggressiveness. Behaviour, 141, 15–27.Google Scholar

Ihle, T. 2011. Kinetic theory of flocking: derivation of hydrodynamic equations. Physical Review E, 83(3), 030901.Google Scholar

Izús, G., Deza, R., Borzi, C., and Wio, H. S. 1997. Global analysis of pattern selection and bifurcations in monostable reaction-diffusion systems. Physica A: Statistical Mechanics and Its Applications, 237(1–2), 135–149.Google Scholar

Jankowitz, W. J., Van Rooyen, M. W., Shaw, D., Kaumba, J. S., and Van Rooyen, N. 2008. Mysterious circles in the Namib Desert. South African Journal of Botany, 74(2), 332–334.Google Scholar

Jiang, L., Giuggioli, L., Perna, A., Escobedo, R., Lecheval, V., Sire, C., Han, Z., and Theraulaz, G. 2017. Identifying influential neighbors in animal flocking. PLoS Computational Biology, 13(11).Google Scholar

Kac, M. 1959. Probability and Related Topics in Physical Sciences. Vol. 1. Providence, RI: American Mathematical Society.Google Scholar

Kac, M., Uhlenbeck, G. E., and Hemmer, P. C. 1963. On the van der Waals theory of the vapor-liquid equilibrium. I. Discussion of a one-dimensional model. Journal of Mathematical Physics, 4(2), 216–228.Google Scholar

Kalcounis-Rüppell, M. C., and Ribble, D. O. 2007. A phylogenetic analysis of the breeding systems of Neotomine–Peromyscine rodents. Pages 68–85 of: Wolff, J., and Sherman, P. W. (eds.), Rodent Societies: An Ecological and Evolutionary Perspective. Chicago: University of Chicago Press.Google Scholar

Kantelhardt, J. W., Zschiegner, S. A., Koscielny-Bunde, E., Havlin, S., Bunde, A., and Stanley, H. E. 2002. Multifractal detrended fluctuation analysis of nonstationary time series. Physica A: Statistical Mechanics and Its Applications, 316(1–4), 87–114.Google Scholar

Kapfer, S. C., and Krauth, W. 2015. Two-dimensional melting: from liquid-hexatic coexistence to continuous transitions. Physical Review Letters, 114, 035702.Google Scholar

Kassner, K. 1996. Pattern Formation in Diffusion-Limited Crystal Growth. Singapore: World Scientific.CrossRef Google Scholar

Katz, Y., Tunstrøm, K., Ioannou, C. C., Huepe, C., and Couzin, I. D. 2011. Inferring the structure and dynamics of interactions in schooling fish. Proceedings of the National Academy of Sciences USA, 108(46), 18720–18725.Google Scholar

Kays, R., Crofoot, M. C., Jetz, W., and Wikelski, M. 2015. Terrestrial animal tracking as an eye on life and planet. Science, 348(6240), aaa2478.Google Scholar

Keeling, M. J., and Rohani, P. 2011. Modeling Infectious Diseases in Humans and Animals. Princeton, NJ: Princeton University Press.Google Scholar

Keller, E. F., and Segel, L. A. 1971. Traveling bands of chemotactic bacteria: a theoretical analysis. Journal of Theoretical Biology, 30(2), 235–248.Google Scholar

Kenkre, V. M. 1974. Coupled wave-like and diffusive motion of excitons. Physics Letters A, 47, 119–120.Google Scholar

Kenkre, V. M. 1977a. The generalized master equation and its applications. Pages 441–461 of: Landman, U. (ed.), Statistical Mechanics and Statistical Methods in Theory and Application. New York: Plenum.Google Scholar

Kenkre, V. M. 1977b. Master-equation theory of the effect of vibrational relaxation on intermolecular transfer of electronic excitation. Physical Review A, 16, 766–776.Google Scholar

Kenkre, V. M. 1980. Theory of exciton annihilation in molecular crystals. Physical Review B, 22, 2089–2098.Google Scholar

Kenkre, V. M. 1981. Validity of the bilinear rate equation for exciton annihilation and expressions for the annihilation constant. Zeitschrift für Physik B Condensed Matter, 43(3), 221–227.Google Scholar

Kenkre, V. M. 1982a. The master equation approach: coherence, energy transfer, annihilation, and relaxation. Pages 1–109 of: Hoehler, G. (ed.), Exciton Dynamics in Molecular Crystals and Aggregates. Berlin: Springer.Google Scholar

Kenkre, V. M. 1982b. A theoretical approach to exciton trapping in systems with arbitrary trap concentration. Chemical Physics Letters, 93(3), 260–263.Google Scholar

Kenkre, V. M. 1989. The quantum nonlinear dimer and extensions. In: Pnevmatikos, S., Bountis, T., and Pnevmatikos, S. (eds.), Singular Behaviour and Nonlinear Dynamics. London: World Scientific.Google Scholar

Kenkre, V. M. 1994. Proceedings of the Granular Material Symposium. Pages BB 6.5.1–8 of: Sen, S., and Hunt, M. L. (eds.), Polarons and Applications, vol. 627. Warrendale, PA: MRS.Google Scholar

Kenkre, V. M. 1998. Four stages in the study of electron-phonon interactions. Journal of Luminescence, 76 /77, 511–517.Google Scholar

Kenkre, V. M. 2001a. Spatial memories and correlation functions in the theory of stress distribution in granular materials. Granular Matter, 3(1–2), 23–28.Google Scholar

Kenkre, V. M. 2001b. Theory of stress distribution in granular materials: the memory formalism. Pages BB6.5.1-8 of: Surajit, S., and Hunt, M. L. (eds.), Materials Research Society conference proceedings on the granular state, vol. 627. Cambridge, UK: Cambridge University Press.Google Scholar

Kenkre, V. M. 2003. Memory formalism, nonlinear techniques, and kinetic equation approaches. Pages 63–103 of: Kenkre, V. M., and Lindenberg, K. (eds.), AIP conference proceedings on Modern Challenges in Statistical Mechanics: Patterns, Noise, and the Interplay of Nonlinearity and Complexity, vol. 658. Melville, NY: American Institute of Physics.Google Scholar

Kenkre, V. M. 2004. Results from variants of the Fisher equation in the study of epidemics and bacteria. Physica A: Statistical Mechanics and Its Applications, 342, 242–248.Google Scholar

Kenkre, V. M. 2005. Statistical mechanical considerations in the theory of the spread of the Hantavirus. Physica A: Statistical Mechanics and Its Applications, 356, 121–126.Google Scholar

Kenkre, V. M., and Campbell, D. K. 1986. Self-trapping on a dimer: time-dependent solutions of a discrete nonlinear Schrödinger equation. Physical Review B, 34(7), 4959.Google Scholar

Kenkre, V. M., Endicott, M. R., Glass, S. J., and Hurd, A. J. 1996. A theoretical model for compaction of granular materials. Journal of the American Ceramic Society, 79(12), 3045–3054.Google Scholar

Kenkre, V. M., Giuggioli, L., Abramson, G., and Camelo-Neto, G. 2007. Theory of Hantavirus infection spread incorporating localized adult and itinerant juvenile mice. European Physics Journal B, 55, 461–470.Google Scholar

Kenkre, V. M., and Knox, R. S. 1974a. Generalized-master-equation theory of excitation transfer. Physical Review B, 9, 5279–5290.Google Scholar

Kenkre, V. M., and Knox, R. S. 1974b. Theory of fast and slow excitation transfer rates. Physical Review Letters, 33(14), 803.Google Scholar

Kenkre, V. M., and Kumar, N. 2008. Nonlinearity in bacterial population dynamics: proposal for experiments for the observation of abrupt transitions in patches. Proceedings of the National Academy of Sciences USA, 105(48), 18752–18757.CrossRef Google Scholar PubMed

Kenkre, V. M., and Kuperman, M. N. 2003. Applicability of the Fisher equation to bacterial population dynamics. Physical Review E, 67(5), 051921.Google Scholar

Kenkre, V. M., and Lindenberg, K. 2003. Modern Challenges in Statistical Mechanics: Patterns, Noise, and the Interplay of Nonlinearity and Complexity. Vol. 658, Conference Proceedings. Melville, NY: American Institute of Physics.Google Scholar

Kenkre, V. M., Montroll, E. W., and Shlesinger, M. F. 1973. Generalized master equations for continuous-time random walks. Journal of Statistical Physics, 9, 45–50.Google Scholar

Kenkre, V. M., Parmenter, R. R., Peixoto, I. D., and Sadasiv, L. 2005. A theoretical framework for the analysis of the West Nile virus epidemic. Mathematical and Computer Modelling, 42(3–4), 313–324.Google Scholar

Kenkre, V. M., and Parris, P. E. 1983. Exciton trapping and sensitized luminescence: a generalized theory for all trap concentrations. Physical Review B, 27(6), 3221.Google Scholar

Kenkre, V. M., and Reineker, P. 1982. Exciton Dynamics in Molecular Crystals and Aggregates. Vol. 94, Springer Tracts in Modern Physics. Berlin: Springer.Google Scholar

Kenkre, V. M., Scott, J. E., Pease, E. A., and Hurd, A. J. 1998. Nonlocal approach to the analysis of the stress distribution in granular systems. I. Theoretical framework. Physical Review E, 57(5), 5841–5849.Google Scholar

Kenkre, V. M., and Sevilla, F. J. 2007. Thoughts about anomalous diffusion: time-dependent coefficients versus memory functions. Pages 147–160 of: Ali, T. S., and Sinha, K. B. (eds.), Contributions to Mathematical Physics: A Tribute to Gerard G. Emch. New Delhi: Hindustani Book Agency.Google Scholar

Kenkre, V. M., and Sugaya, S. 2014. Theory of the transmission of infection in the spread of epidemics: interacting random walkers with and without confinement. Bulletin of Mathematical Biology, 76(12), 3016–3027.Google Scholar

Kenkre, V. M., and Tsironis, G. P. 1987. Nonlinear effects in quasielastic neutron scattering: exact line-shape calculation for a dimer. Physical Review B, 35(4), 1473.Google Scholar

Kenkre, V. M., and Van Horn, H. M. 1981. Annihilations of stationary particles on a lattice. Physical Review A, 23(6), 3200.Google Scholar

Kenkre, V. M., and Wong, Y. M. 1981. Effect of transport coherence on trapping: quantum-yield calculations for excitons in molecular crystals. Physical Review B, 23(8), 3748.Google Scholar

Kermack, W. O., and McKendrick, A. G. 1927. A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London A, 115(772), 700–721.Google Scholar

Kessler, D. A., and Levine, H. 1993. Pattern formation in Dictyostelium via the dynamics of cooperative biological entities. Physical Review E, 48(6), 4801.Google Scholar

Kierstead, H., and Slobodkin, L. B. 1953. The size of water masses containing plankton blooms. Journal of Marine Research, 12(1), 141–147.Google Scholar

Kinezaki, N., Kawasaki, K., Takasu, F., and Shigesada, N. 2003. Modeling biological invasions into periodically fragmented environments. Theoretical Population Biology, 64(3), 291–302.Google Scholar

Kleman, M., and Laverntovich, O. D. 2007. Soft Matter Physics: An Introduction. New York: Springer.Google Scholar

Kokko, H., and Sutherland, W. J. 2001. Ecological traps in changing environments: ecological and evolutionary consequences of a behaviourally mediated Allee effect. Evolutionary Ecology Research, 3(5), 603–610.Google Scholar

Kolmogorov, A. N., Petrovsky, I., and Piskunov, N. 1937 . Étude de l’équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique. Bulletin of the University of Moskow, Ser. Internat., Sec. A, 1, 1–25.Google Scholar

Kosterlitz, D. J., and Thouless, J. M. 1973. Ordering, metastability and phase transitions in two-dimensional systems. Journal of Physics C: Solid State Physics, 1181(7), 1181–1203.Google Scholar

Kot, M. 2001. Elements of Mathematical Ecology. Cambridge, UK: Cambridge University Press.Google Scholar

Kozel, R. M., and Fleharty, E. D. 1979. Movements of rodents across roads. Southwestern Naturalist, 24(2), 239–248.Google Scholar

Krebs, J. R., and Davies, N. B. 1987. An Introduction to Behavioral Ecology. Oxford, UK: Blackwell Scientific Publications.Google Scholar

Kuenzi, A. J., Morrison, M. L., Swann, D. E., Hardy, P. C., and Downard, G. T. 1999. A longitudinal study of Sin Nombre virus prevalence in rodents, southeastern Arizona. Emerging Infectious Diseases, 5(1), 113.Google Scholar

Kumar, N., and Kenkre, V. M. 2011. Effects of gradual spatial variation in resources on population extinction: analytic calculations for abrupt transitions. Physica A: Statistical Mechanics and Its Applications, 390(2), 257–262.CrossRef Google Scholar

Kumar, N., Kuperman, M. N., and Kenkre, V. M. 2009b. Theory of possible effects of the Allee phenomenon on the population of an epidemic reservoir. Physical Review E, 79(4), 041902.Google Scholar

Kumar, N., Parmenter, R. R., and Kenkre, V. M. 2010. Extinction of refugia of hantavirus infection in a spatially heterogeneous environment. Physical Review E, 82(1), 011920.Google Scholar

Kumar, N., Viswanathan, G. M., and Kenkre, V. M. 2009a. Hurst exponents for interacting random walkers obeying nonlinear Fokker–Planck equations. Physica A: Statistical Mechanics and Its Applications, 388(18), 3687–3694.Google Scholar

Kuramoto, Y. 1984. Chemical Oscillations, Waves, and Turbulence. Berlin: Springer.Google Scholar

Lakatos-Lindenberg, K., Hemenger, R. P., and Pearlstein, R. M. 1972. Solutions of master equations and related random walks on quenched linear chains. Journal of Chemical Physics, 56(10), 4852–4867.Google Scholar

Landau, L. D. 1933. Electron motion in crystal lattices. Physikalische Zeitschrift der Sowjetunion, 3, 664.Google Scholar

Landman, U., Montroll, E. W., and Shlesinger, M. F. 1977. Random walks and generalized master equations with internal degrees of freedom. Proceedings of the National Academy of Sciences USA, 74(2), 430–433.Google Scholar

Lee, C. T., Hoopes, M. F., Diehl, J., Gilliland, W., Huxel, G., Leaver, E. V., McCann, K., Umbanhowar, J., and Mogilner, A. 2001. Non-local concepts and models in biology. Journal of Theoretical Biology, 210(2), 201–219.Google Scholar

Lewis, M. A., and Murray, J. D. 1993. Modelling territoriality and wolf-deer interactions. Ecology, 366, 738–740.Google Scholar

Likos, C. N. 2001. Effective interactions in soft condensed matter physics. Physics Reports, 348(4–5), 267–439.Google Scholar

Lin, A. L. 2003. Resonant Chemical Oscillations: Pattern Formation in Reaction-Diffusion Systems. Pages 315–328 of: Kenkre, V. M., and Lindenberg, K. (eds.), AIP conference proceedings on Modern Challenges in Statistical Mechanics: Patterns, Noise, and the Interplay of Nonlinearity and Complexity, vol. 658. Melville, NY: American Institute of Physics.Google Scholar

Lin, A. L., Mann, B. A., Torres-Oviedo, G., Lincoln, B., Käs, J., and Swinney, H. L. 2004. Localization and extinction of bacterial populations under inhomogeneous growth conditions. Biophysical Journal, 87(1), 75–80.Google Scholar

Lindner, M., Nir, G., Vivante, A., Young, I. T., and Garini, Y. 2013. Dynamic analysis of a diffusing particle in a trapping potential. Physical Review E, 87(2), 022716.Google Scholar

Livesay, D. R., Jambeck, P., Rojnuckarin, A., and Subramaniam, S. 2003. Conservation of electrostatic properties within enzyme families and superfamilies. Biochemistry, 42(12), 3464–3473.Google Scholar

Long, J. A., and Nelson, T. A. 2012. Time geography and wildlife home range delineation. Journal of Wildlife Management, 76(2), 407–413.Google Scholar

Lopez, U., Gautrais, J., Couzin, I. D., and Theraulaz, G. 2012. From behavioural analyses to models of collective motion in fish schools. Interface Focus, 2(6), 693–707.Google Scholar

Lotka, A. J. 1926. Elements of physical biology. Science Progress in the Twentieth Century (1919–1933), 21(82), 341–343.Google Scholar

Ludwig, D., Aronson, D. G., and Weinberger, H. F. 1979. Spatial patterning of the spruce budworm. Journal of Mathematical Biology, 8(3), 217–258.Google Scholar

Lukeman, R., Li, Y.-X., and Edelstein-Keshet, L. 2010. Inferring individual rules from collective behavior. Proceedings of the National Academy of Sciences USA, 107(28), 12576–12580.Google Scholar

Lyons, A. J., Turner, W. C., and Getz, W. M. 2013. Home range plus: a space-time characterization of movement over real landscapes. Movement Ecology, 1(2).Google Scholar

MacArthur, R. H, and Wilson, E. O. 1967. The Theory of Island Biogeography. Princeton, NJ: Princeton University Press.Google Scholar

Madras, N., and Slade, G. 2013. The Self-Avoiding Walk. Berlin: Springer.Google Scholar

Maher, C. A., and Lott, D. F. 1995. Definitions of territoriality used in the study of variation in vertebrate spacing systems. Animal Behaviour, 49, 1581–1597.Google Scholar

Mainardi, F., Luchko, Y., and Pagnini, G. 2001. The fundamental solution of the space-time fractional diffusion equation. Fractional Calculus and Applied Analysis, 4, 153–192.Google Scholar

Mandelbrot, B. B., and Van Ness, J. W. 1968. Fractional Brownian motions, fractional noises and applications. SIAM Review, 10(4), 422–437.Google Scholar

Mann, B. 2001. Spatial phase-transitions in bacterial growth. PhD thesis, University of Texas, Austin, TX.Google Scholar

Manne, K. K., Hurd, A. J., and Kenkre, V. M. 2000. Nonlinear waves in reaction-diffusion systems: The effect of transport memory. Physical Review E, 61(4), 4177.Google Scholar

Marchetti, M. C., Joanny, J.-F., Ramaswamy, S., Liverpool, T. B., Prost, J., Rao, M., and Simha, R. A. 2013. Hydrodynamics of soft active matter. Reviews of Modern Physics, 85(3), 1143.Google Scholar

Marfin, A. A., Petersen, L. R., Eidson, M., Miller, J., Hadler, J., Farello, C., Werner, B., Campbell, G. L., Layton, M., Smith, P., Bresnitz, E., Cartter, M., Scaletta, J., Obiri, G., Bunning, M., Craven, R. C., Roehrig, J. T., Julian, K. G., Hinten, S. R., Gubler, D. J., and the ArboNET Cooperative Surveillance Group. 2001. Widespread West Nile virus activity, eastern United States, 2000. Emerging Infectious Diseases, 7(4), 730.Google Scholar

Maude, G. 2010. The Spatial Ecology and Foraging Behaviour of the Brown Hyaena (Hyaena brunnea). PhD thesis, University of Bristol, Bristol, UK.Google Scholar

May, R. M. 2001. Stability and Complexity in Model Ecosystems. 2nd ed. Princeton, NJ: Princeton University Press.Google Scholar

McInnis, D. 2007. Applications of Nonlinear Science and Kinetic Equations to the Theory of the Spread of Epidemics. PhD thesis, University of New Mexico, Albuquerque, NM.Google Scholar

McKane, A. J., and Newman, T. J. 2004. Stochastic models in population biology and their deterministic analogs. Physical Review E, 70, 041902.Google Scholar

McKean, H. P. Jr. 1970. Nagumo’s equation. Advances in Mathematics, 4(3), 209–223.Google Scholar

Méndez, V., Fedotov, S., and Horsthemke, W. 2010. Reaction-Transport Systems: Mesoscopic Foundations, Fronts, and Spatial Instabilities. Berlin: Springer.Google Scholar

Méndez, V., Campos, D., and Bartumeus, F. 2016. Stochastic Foundations in Movement Ecology. Berlin: Springer.Google Scholar

Méndez, V., and Campos, D. 2008. Population extinction and survival in a hostile environment. Physical Review E, 77(2), 022901.Google Scholar

Mermin, N. D. 1968. Crystalline order in two dimensions. Physical Review, 176(1), 250.Google Scholar

Mermin, N. D., and Wagner, H. 1966. Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Physical Review Letters, 17(22), 1133.Google Scholar

Metzler, R., Jeon, J.-H., Cherstvy, A. G., and Barkai, E. 2014. Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking. Physical Chemistry Chemical Physics, 16(44), 24128–24164.Google Scholar

Metzler, R., and Klafter, J. 2000. The random walks guide to anomalous diffusion: a fractional dynamics approach. Physics Reports, 339, 1–77.Google Scholar

Mikhailov, A. S., and Zanette, D. H. 1999. Noise-induced breakdown of coherent collective motion in swarms. Physical Review E, 60, 4571–4575.Google Scholar

Mills, J. N., Ksiazek, T. G., Peters, C. J., and Childs, J. E. 1999a. Long-term studies of hantavirus reservoir populations in the southwestern United States: a synthesis. Emerging Infectious Diseases, 5(1), 135.Google Scholar

Mills, J. N., Yates, T. L., Ksiazek, T. G., Peters, C. J., and Childs, J. E. 1999b. Long-term studies of hantavirus reservoir populations in the southwestern United States: rationale, potential, and methods. Emerging Infectious Diseases, 5(1), 95.Google Scholar

Mogilner, A., and Edelstein-Keshet, L. 1995. Selecting a common direction I. How orientational order can arise from simple contact responses between interacting cells. Journal of Mathematical Biology, 33(6), 619–660.Google Scholar

Mogilner, A., and Edelstein-Keshet, L. 1996. Spatio-angular order in populations of self-aligning objects: formation of oriented patches. Physica D: Nonlinear Phenomena, 89(3–4), 346–367.Google Scholar

Mogilner, A., and Edelstein-Keshet, L. 1999. A non-local model for a swarm. Journal of Mathematical Biology, 38(6), 534–570.Google Scholar

Mogilner, A., Edelstein-Keshet, L., and Ermentrout, G. B. 1996. Selecting a common direction. Journal of Mathematical Biology, 34(8), 811–842.Google Scholar

Mollison, D. 1977. Spatial contact models for ecological and epidemic spread. Journal of the Royal Statistical Society: Series B, 39(3), 283–313.Google Scholar

Mollison, D. 1991. Dependence of epidemic and population velocities on basic parameters. Mathematical Biosciences, 107, 255–287.Google Scholar

Montroll, E. W. 1964. Random walks on lattices. Pages 193–220 of: Bellman, R. (ed.), Stochastic Processes in Mathematical Physics and Engineering. Proceedings of Symposia in Applied Mathematics, vol. 16. Providence, RI: American Mathematical Society.Google Scholar

Montroll, E. W. 1967. On nonlinear processes involving population growth and diffusion. Journal of Applied Probability, 4(2), 281–290.Google Scholar

Montroll, E. W. 1969. Random walks on lattices containing traps. Page 6 of: Physical Society of Japan Journal Supplement, Proceedings of the International Conference on Statistical Mechanics, vol. 26.Google Scholar

Montroll, E. W., and Potts, R. B. 1955. Effect of Defects on Lattice Vibrations. Physical Review, 100(2), 525–543.Google Scholar

Montroll, E. W., and Weiss, G. H. 1965. Random walks on Lattices II. Journal of Mathematical Physics, 6(2), 167–181.Google Scholar

Montroll, E. W., and West, B. J. 1979. On an enriched collection of stochastic processes. Pages 61–175 of: Montroll, E. W., and Lebowitz, J. J. (eds.), Studies in Statistical Mechanics: Vol. VII. Fluctuation Phenomena. Amsterdam: North Holland Publishing.Google Scholar

Moorcroft, P. R., and Lewis, M. A. 2006. Mechanistic Home Range Analysis. Princeton, NJ: Princeton University Press.Google Scholar

Mora, T., and Bialek, W. 2011. Are biological systems poised at criticality? Journal of Statistical Physics, 144(2), 268–302.Google Scholar

Moussaïd, M., Helbing, D., and Theraulaz, G. 2011. How simple rules determine pedestrian behavior and crowd disasters. Proceedings of the National Academy of Sciences USA, 108(17), 6884–6888.Google Scholar

Murray, J. D. 2003a. Mathematical Biology: I. An Introduction. 3rd ed. Berlin: Springer.Google Scholar

Murray, J. D. 2003b. Mathematical Biology: II. Spatial Models and Biomedical Applications. 3rd ed. Berlin: Springer.Google Scholar

Nagy, M., Akos, Z., Biro, D., and Vicsek, T. 2010. Hierarchical group dynamics in pigeon flocks. Nature, 464, 890–893.Google Scholar

Nagy, M., Daruka, I., and Vicsek, T. 2007. New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion. Physica A: Statistical Mechanics and Its Applications, 373, 445–454.Google Scholar

Namboodiri, V. M. K., Levy, J. M., Mihalas, S., Sims, D. W., and Shuler, M. G. H. 2016. Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework. Proceedings of the National Academy of Sciences USA, 113(31), 8747–8752.Google Scholar

Nasci, R. S., Savage, H. M., White, D. J., Miller, J. R., Cropp, B. C., Godsey, M. S., Kerst, A. J., Bennett, P., Gottfried, K., and Lanciotti, R. S. 2001. West Nile virus in overwintering Culex mosquitoes, New York City, 2000. Emerging Infectious Diseases, 7(4), 742.Google Scholar

Nathan, R. M., Getz, W. M., Revilla, E., Holyoak, M., Kadmon, R., Saltz, D., and Smouse, P. E. 2008. A movement ecology paradigm for unifying organismal movement research. Proceedings of the National Academy of Sciences USA, 105, 19052–19059.Google Scholar

Nayfeh, A. H. 2008. Perturbation Methods. New York: John Wiley & Sons.Google Scholar

Nelson, D. R., and Shnerb, N. M. 1998. Non-Hermitian localization and population biology. Physical Review E, 58(2), 1383.Google Scholar

Newell, A. C. 1997. The dynamics and analysis of patterns. Pages 201–268 of: Nijhout, H. F., Nadel, L., and Stein, D. (eds.), Pattern Formation in the Physical and Biological Sciences, vol. 5. Boca Raton, FL: CRC Press.Google Scholar

Newman, K., and Borchers, D. L. 2014. Modelling Population Dynamics: Model Formulation, Fitting and Assessment Using State-Space Methods. Methods in Statistical Ecology. New York: Springer.Google Scholar

Newton, I. 1992. Experiments on the limitation of bird numbers by territorial behaviour. Biological Reviews, 67, 129–173.Google Scholar

Nice, M. M. 1941. The role of territory in bird life. American Naturalist, 26(3), 441–487.Google Scholar

Nichol, S. T., Spiropoulou, C. F., Morzunov, S., Rollin, P. E., Ksiazek, T. G., Feldmann, H., Sanchez, A., Childs, J., Zaki, S., and Peters, C. J. 1993. Genetic identification of a hantavirus associated with an outbreak of acute respiratory illness. Science, 262(5135), 914–917.Google Scholar

Nicolis, G. 1995. Introduction to Nonlinear Science. Cambridge, UK: Cambridge University Press.Google Scholar

Nigg, B. M., MacIntosh, B. R., and Mester, J. 2000. Biomechanics and Biology Of Movement. Champaign, IL: Human Kinetics Publishers.Google Scholar

Nimzowitsch, A. 1930. My System: A Treatise on Chess. Vol. 5. New York: Three Rivers Press.Google Scholar

Niwa, H.-S. 1994. Self-organizing dynamic model of fish schooling. Journal of Theoretical Biology, 171(2), 123–136.Google Scholar

Okubo, A. 1980. Diffusion and Ecological Problems: Mathematical Models. Vol. 10 Biomathematics. Berlin: Springer.Google Scholar

Okubo, A., Grünbaum, D., and Edelstein-Keshet, L. 2001. The dynamics of animal grouping. Pages 197–237 of: Diffusion and Ecological Problems: Modern Perspectives. New York: Springer.Google Scholar

Okubo, A., and Levin, S. A. 2001. Diffusion and Ecological Problems: Modern Perspectives. 2nd ed. New York: Springer.Google Scholar

Olfati-Saber, R. 2006. Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Transactions on Automatic Control, 51(3), 401–420.Google Scholar

Ovaskainen, O. 2004. Habitat-specific movement parameters estimated using mark– recapture data and a diffusion model. Ecology, 85(1), 242–257.Google Scholar

Park, S., Wolanin, P. M., Yuzbashyan, E. A., Lin, H., Darnton, N. C., Stock, J. B., Silberzan, P., and Austin, R. 2003. Influence of topology on bacterial social interaction. Proceedings of the National Academy of Sciences USA, 100(24), 13910–13915.Google Scholar

Parmenter, C. A., Yates, T. L., Parmenter, R. R., and Dunnum, J. L. 1999. Long-term field studies of small mammals for hantavirus prevalence: statistical sensitivity for detection of spatial and temporal patterns in rodent population densities. Emerging Infectious Diseases, 5, 118–25.Google Scholar

Parmenter, R. R., and MacMahon, J. A. 1983. Factors determining the abundance and distribution of rodents in a shrub-steppe ecosystem: the role of shrubs. Oecologia, 59, 145–156.Google Scholar

Parris, P. E., Candia, J., and Kenkre, V. M. 2008. Random-walk access times on partially disordered complex networks: an effective medium theory. Physical Review E, 77(6), 061113.Google Scholar

Parris, P. E, and Kenkre, V. M. 2005. Traversal times for random walks on small-world networks. Physical Review E, 72(5), 056119.Google Scholar

Parrish, J. K., and Hamner, W. M. 1997. Animal Groups in Three Dimensions: How Species Aggregate. Cambridge, UK: Cambridge University Press.Google Scholar

Pastor, J. 2011. Mathematical Ecology of Populations and Ecosystems. Chichester, UK: John Wiley & Sons.Google Scholar

Pearce, D. J. G., Miller, A. M., Rowlands, G., and Turner, M. S. 2014. Role of projection in the control of bird flocks. Proceedings of the National Academy of Sciences USA, 111(29), 10422–10426.Google Scholar

Peixoto, I. D., Giuggioli, L., and Kenkre, V. M. 2005. Arbitrary nonlinearities in convective population dynamics with small diffusion. Physical Review E, 72(4), 041902.Google Scholar

Pekar, S. I. 1954. Untersuchung über die Elektronentheorie der Kristalle, Berlin, Akad. Berlin: Akademie Verlag.Google Scholar

Perry, N. 2005. Experimental validation of a critical domain size in reaction–diffusion systems with Escherichia coli populations. Journal of the Royal Society Interface, 2(4), 379–387.Google Scholar

Petrovskii, S. V., and Li, B.-L. 2005. Exactly Solvable Models of Biological Invasion. Boca Raton, FL: Chapman and Hall/CRC.Google Scholar

Pimentel, J. A., Aldana, M., Huepe, C., and Larralde, H. 2008. Intrinsic and extrinsic noise effects on phase transitions of network models with applications to swarming systems. Physical Review E, 77(6), 061138.Google Scholar

Podlubny, I. 1999. Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. San Diego, CA: Academic Press.Google Scholar

Pope, M., and Swenberg, C. E. 1999. Electronic Processes in Organic Crystals and Polymers. 2nd ed. New York: Oxford University Press.Google Scholar

Porfiri, M., Stilwell, D. J., Bollt, E. M., and Skufca, J. D. 2006. Random talk: Random walk and synchronizability in a moving neighborhood network. Physica D: Nonlinear Phenomena, 224(1–2), 102–113.Google Scholar

Poston, T., and Stewart, I. 1978. Catastrophe Theory and Its Applications. London: Pitman Publishing.Google Scholar

Potts, J. R., Harris, S., and Giuggioli, L. 2012. Territorial dynamics and stable home range formation for central place foragers. PLoS ONE, 7(3), e34033.Google Scholar

Potts, J. R., Harris, S., and Giuggioli, L. 2013. Quantifying behavioral changes in territorial animals caused by sudden population declines. American Naturalist, 182(3).Google Scholar

Powell, R. A., and Mitchell, M. S. 2012. What is a home range? Journal of Mammalogy, 93(4).Google Scholar

Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T. 1989. Numerical Recipes. Vol. 3. Cambridge, UK: Cambridge University Press.Google Scholar

Puri, S. 1991. Singular-perturbation analysis of the Fisher equation. Physical Review A, 43(12), 7031.Google Scholar

Puri, S., and Wiese, K. J. 2003. Perturbative linearization of reaction–diffusion equations. Journal of Physics A: Mathematical and General, 36(8), 2043.Google Scholar

Pyke, G. H. 1979. The economics of territory size and time budget in the golden-winged sunbird. American Naturalist, 114, 131–145.Google Scholar

Pyke, G. H. 2015. Understanding movements of organisms: it’s time to abandon the Lévy foraging hypothesis. Methods in Ecology and Evolution, 6(1), 1–16.Google Scholar

Qi, W., Gantapara, A. P., and Dijkstra, M. 2014. Two-stage melting induced by dislocations and grain boundaries in monolayers of hard spheres. Soft Matter, 10(30), 5449–5457.Google Scholar

Quinn, G. P., Keough, M.J., et al. 2002. Experimental Design and Data Analysis for Biologists. New York: Cambridge University Press.Google Scholar

Quinn, R. A., and Goree, J. 2001. Experimental test of two-dimensional melting through disclination unbinding. Physical Review E, 64(5), 051404.Google Scholar

Rabinovich, M. I., Ezersky, A. B., and Weidman, P. D. 2000. The Dynamics of Patterns. Singapore: World Scientific.Google Scholar

Raghib, M., Levin, S. A., and Kevrekidis, I. G. 2010. Multiscale analysis of collective motion and decision-making in swarms: an advection–diffusion equation with memory approach. Journal of Theoretical Biology, 264(3), 893–913.Google Scholar

Ramaswamy, S. 2010. The mechanics and statistics of active matter. Annual Review of Condensed Matter Physics, 1(1), 323–345.Google Scholar

Rappel, W.-J., Nicol, A., Sarkissian, A., Levine, H., and Loomis, W. F. 1999. Self-organized vortex state in two-dimensional Dictyostelium dynamics. Physical Review Letters, 83(6), 1247.Google Scholar

Redner, S. 2001. A Guide to First-Passage Processes. Cambridge, UK: Cambridge University Press.Google Scholar

Redner, S., and Ben-Avraham, D. 1990. Nearest-neighbour distances of diffusing particles from a single trap. Journal of Physics A: Mathematical and General, 23(22), L1169– L1173.Google Scholar

Reichl, L. E. 2009. A Modern Course in Statistical Physics. 3rd ed. Hoboken, NJ: John Wiley & Sons.Google Scholar

Renshaw, E. 1993. Modelling Biological Populations in Space and Time. Vol. 11. Cambridge, UK: Cambridge University Press.Google Scholar

Reynolds, A. 2015. Liberating Lévy walk research from the shackles of optimal foraging. Physics of Life Reviews, 14, 59–83.Google Scholar

Reynolds, C. W. 1987. Flocks, herds and schools: a distributed behavioral model. ACM SIGGRAPH Computer Graphics, 21(4), 25–34.Google Scholar

Ribble, D. O., and Stanley, S. 1998. Home ranges and social organization of syntopic Peromyscus boylii and P. truei. Journal of Mammalogy, 79(3), 932–941.Google Scholar

Risken, H. 1984. The Fokker–Planck Equation: Methods of Solution and Applications. Berlin: Springer Series in Synergetics, vol. 18.Google Scholar

Robertson, G. E., Caldwell, G. E., Hamill, J., Kamen, G., and Whittlesey, S. 2013. Research Methods in Biomechanics. Champaign, IL: Human Kinetics Publishers.Google Scholar

Romanczuk, P., Bär, M., Ebeling, W., Lindner, B., and Schimansky-Geier, L. 2012. Active Brownian particles. The European Physical Journal Special Topics, 202(1), 1–162.Google Scholar

Rubenstein, D. I. 1981. Individual variation and competition in the Everglades pygmy sunfish. Journal of Animal Ecology, 50, 337–350.Google Scholar

Rubin, R. J., and Weiss, G. H. 1982. Random walks on lattices. The problem of visits to a set of points revisited. Journal of Mathematical Physics, 23(2), 250–253.Google Scholar

Ruefenacht, B., and Knight, R. L. 1995. Influences of corridor continuity and width on survival and movement of deermice Peromyscus maniculatus. Biological Conservation, 71(3), 269–274.Google Scholar

Saichev, A. I., and Zaslavsky, G. M. 1997. Fractional kinetic equations: solutions and applications. Chaos: An Interdisciplinary Journal of Nonlinear Science, 7(4), 753–764.Google Scholar

Sarvaharman, S., Heiblum-Robles, A., and Giuggioli, L. 2019. From micro-to-macro: how the movement statistics of individual walkers affect the formation of segregated territories in the territorial random walk model. Frontiers in Physics, 7, 129.Google Scholar

Satomi, S. 2016. The Smoluchowski Equation in Population Dynamics and the Spread of Infection. PhD thesis, University of New Mexico, Albuquerque, NM.Google Scholar

Scher, H., and Montroll, E. W. 1975. Anomalous transit-time dispersion in amorphous solids. Physical Review B, 12(6), 2455–2477.Google Scholar

Schmaljohn, C., and Hjelle, B. 1997. Hantaviruses: a global disease problem. Emerging Infectious Diseases, 3(2), 95.Google Scholar

Schneider, W. R., and Wyss, W. 1989. Fractional diffusion and wave equations. Journal of Mathematical Physics, 30(1), 134–144.Google Scholar

Scott, J. E., Kenkre, V. M., and Hurd, A. J. 1998. Nonlocal approach to the analysis of the stress distribution in granular systems. II. Application to experiment. Physical Review E, 57(5), 5850–5857.Google Scholar

Seuront, L., and Stanley, H. E. 2014. Anomalous diffusion and multifractality enhance mating encounters in the ocean. Proceedings of the National Academy of Sciences USA, 111(6), 2206–2211.Google Scholar

Sevilla, F. J., Dossetti, V., and Heiblum Robles, A. 2014. Synchronization and collective motion of globally coupled Brownian particles. Journal of Statistical Mechanics: Theory and Experiment, 2014(12), P12025.Google Scholar

Shigesada, N., and Kawasaki, K. 1997. Biological Invasions: Theory and Practice. Oxford, UK: Oxford University Press.Google Scholar

Shigesada, N., Kohkichi, K., and Teramoto, E. 1986. Traveling periodic waves in heterogeneous environments. Theoretical Population Biology, 30, 143–160.Google Scholar

Shlesinger, M. F. 1974. Asymptotic solutions of continuous-time random walks. Journal of Statistical Physics, 10(5), 421–434.Google Scholar

Shlesinger, M. F., and Klafter, J. 1986. Lévy walks versus Lévy flights. Pages 279–283 of: Stanley, H. E., and Ostrowsky, N. (eds.), On Growth and Form: Fractal and Non-Fractal Patterns in Physics. Dordrecht, Netherlands: Martinus Nijhoff Publishers.Google Scholar

Shlesinger, M. F., Klafter, J., and West, B. J. 1986. Lévy walks with applications to turbulence and chaos. Physica A: Statistical Mechanics and Its Applications, 140(1–2), 212–218.Google Scholar

Shlesinger, M. F., Klafter, J., and Wong, Y. M. 1982. Random walks with infinite spatial and temporal moments. Journal of Statistical Physics, 27(3), 499–512.Google Scholar

Shnerb, N. M. 2000. Extinction of a bacterial colony under forced convection in pie geometry. Physical Review E, 63(1), 011906.Google Scholar

Shugard, W, and Reiss, H. 1976. Derivation of the continuous-time random walk equation in non-homogeneous lattices. Journal of Chemical Physics, 65, 2827.Google Scholar

Sinhuber, M., and Ouellette, N. T. 2017. Phase coexistence in insect swarms. Physical Review Letters, 119(17), 178003.Google Scholar

Sinhuber, M., Van Der Vaart, K., Ni, R., Puckett, J. G., Kelley, D. H., and Ouellette, N. T. 2019. Three-dimensional time-resolved trajectories from laboratory insect swarms. Scientific Data, 6, 190036.Google Scholar

Skellam, J. G. 1951. Random dispersal in theoretical populations. Biometrika, 38, 196–218.Google Scholar

Smoluchowski, M. von. 1916. Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen II. Physikalische Zeitschrift, 17, 585–599.Google Scholar

Sokolov, A., Goldstein, R. E., Feldchtein, F. I., and Aranson, I. S. 2009. Enhanced mixing and spatial instability in concentrated bacterial suspensions. Physical Review E, 80(3), 031903.Google Scholar

Spendier, K., and Kenkre, V. M. 2013. Analytic solutions for some reaction-diffusion scenarios. Journal of Physical Chemistry B, 117(49), 15639–15650.Google Scholar

Spendier, K., Sugaya, S., and Kenkre, V. M. 2013. Reaction-diffusion theory in the presence of an attractive harmonic potential. Physical Review E, 88, 062142.Google Scholar

Stamps, J. A. 1994. Territorial behavior: testing the assumptions. Advances in the Study of Behavior, 23, 173–232.Google Scholar

Stamps, J. A. 1995. Motor learning and the value of familiar space. American Naturalist, 146, 41–58.Google Scholar

Stanley, H. E. 1971. Phase Transitions and Critical Phenomena. Oxford, UK: Clarendon Press.Google Scholar

Steiniger, S., and Hunter, A. J. S. 2013. A scaled line-based kernel density estimator for the retrieval of utilization distributions and home ranges from GPS movement tracks. Ecological Informatics, 13, 1–8.Google Scholar

Stickel, L. F. 1968. Home range and travels. Pages 373–411 of: King, J. A. (ed.), Biology of Peromyscus (Rodentia), Special Publication No. 2. Stillwater, OK: The American Society of Mammalogists.Google Scholar

Strandburg-Peshkin, A., Farine, D. R., Couzin, I. D., and Crofoot, M. C. 2015. Shared decision-making drives collective movement in wild baboons. Science, 348(6241), 1358–1361.Google Scholar

Strandburg-Peshkin, A., Twomey, C. R., Bode, N. W., Kao, A. B., Katz, Y., Ioannou, C. C., Rosenthal, S. B., Torney, C. J., Wu, H., Levin, S. A., and Couzin, I. D. 2013. Visual sensory networks and effective information transfer in animal groups. Current Biology, 23(17), R709–711.Google Scholar

Strausbaugh, L. J., Marfin, A. A., and Gubler, D. J. 2001. West Nile encephalitis: an emerging disease in the United States. Clinical Infectious Diseases, 33(10), 1713–1719.Google Scholar

Strogatz, S. H. 2018. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Boca Raton, FL: CRC Press.Google Scholar

Strömbom, D. 2011. Collective motion from local attraction. Journal of Theoretical Biology, 283(1), 145–151.Google Scholar

Sugaya, S., and Kenkre, V. M. 2018. Analysis of transmission of infection in epidemics: confined random walkers in dimensions higher than one. Bulletin of Mathematical Biology, 80(12), 3106–3126.Google Scholar

Sumpter, D. J. T. 2006. The principles of collective animal behaviour. Philosophical Transactions of the Royal Society B: Biological Sciences, 361(1465), 5–22.Google Scholar

Sumpter, D. J. T. 2010. Collective Animal Behavior. Princeton, NJ: Princeton University Press.Google Scholar

Swinney, H. L., Fitch, V. L., Marlow, D. R., and Dementi, M. A. E. 1996. Emergence and evolution patterns. Pages 51–74 of: Fitch, V. L., and Marlow, D. R. (eds.), Critical Problems in Physics: Proceedings of a Conference Celebrating the 250th Anniversary of Princeton University. Princeton, NJ: Princeton University Press.Google Scholar

Szabo, A., Lamm, G., and Weiss, G. H. 1984. Localized partial traps in diffusion processes and random walks. Journal of Statistical Physics, 34(1–2), 225–238.Google Scholar

Szabó, B., Szöllösi, G. J., Gönci, B., Jurányi, Z., Selmeczi, D., and Vicsek, T. 2006. Phase transition in the collective migration of tissue cells: experiment and model. Physical Review E, 74(6), 061908.Google Scholar

Taylor, C. M., and Hastings, A. 2005. Allee effects in biological invasions. Ecology Letters, 8(8), 895–908.Google Scholar

Taylor, , L. A, Taylor, G. K., Lambert, B., Walker, J. A., Biro, D., and Portugal, S. J. 2019. Birds invest wingbeats to keep a steady head and reap the ultimate benefits of flying together. PLoS Biology, 17(6).Google Scholar

Terman, C. R. 1968. Population dynamics. Pages 412–450 of: King, J. A. (ed.), Biology of Peromyscus (Rodentia), Special Publication No. 2. Stillwater, OK: The American Society of Mammalogists.Google Scholar

Theophilides, C. N., Ahearn, S. C., Grady, S., and Merlino, M. 2003. Identifying West Nile virus risk areas: the dynamic continuous-area space-time system. American Journal of Epidemiology, 157(9), 843–854.Google Scholar

Theraulaz, G., and Bonabeau, E. 1999. A brief history of stigmergy. Artificial Life, 5(2), 97–116.Google Scholar

Thompson, D. W. 1961. On Growth and Form. Cambridge, UK: Cambridge University Press.Google Scholar

Tilman, D., and Kareiva, P. (eds.). 1997. Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions. Vol. 89. Princeton, NJ: Princeton University Press.Google Scholar

Tinnin, D.S. 2003. Testing the Refugia Hypothesis: Population Dynamics of Peromyscus and Hantavirus Seroprevalence across an Elevational Gradient. MPhil thesis, University of New Mexico, Albuquerque, NM.Google Scholar

Tobin, P. C., Berec, L., and Liebhold, A. M. 2011. Exploiting Allee effects for managing biological invasions. Ecology Letters, 14(6), 615–624.Google Scholar

Toner, J., and Tu, Y. 1995. Long-range order in a two-dimensional dynamical XY model: how birds fly together. Physical Review Letters, 75(23), 4326.Google Scholar

Toner, J., and Tu, Y. 1998. Flocks, herds, and schools: a quantitative theory of flocking. Physical Review E, 58(4), 4828.Google Scholar

Toner, J., Tu, Y., and Ramaswamy, S. 2005. Hydrodynamics and phases of flocks. Annals of Physics, 318(1), 170–244.Google Scholar

Touchette, H., Van der Straeten, E., and Just, W. 2010. Brownian motion with dry friction: Fokker–Planck approach. Journal of Physics A: Mathematical and Theoretical, 43(44), 445002.Google Scholar

Toyozawa, Y. 1954. Theory of the electronic polaron and ionization of a trapped electron by an exciton. Progress of Theoretical Physics, 12(4), 421–442.Google Scholar

Trepat, X., Wasserman, M. R., Angelini, T. E., Millet, E., Weitz, D. A., Butler, J. P., and Fredberg, J. J. 2009. Physical forces during collective cell migration. Nature Physics, 5(6), 426–430.Google Scholar

Tsallis, C. 1988. Possible generalization of Boltzmann–Gibbs statistics. Journal of Statistical Physics, 52(1–2), 479–487.Google Scholar

Tunstrøm, K., Katz, Y., Ioannou, C. C., Huepe, C., Lutz, M. J., and Couzin, I. D. 2013. Collective states, multistability and transitional behavior in schooling fish. PLoS Computational Biology, 9(2).Google Scholar

Turchin, P. 1998. Quantitative Analysis of Movement: Measuring and Modelling Population Redistribution in Animals and Plants. Sunderland, MA: Sinauer Associates.Google Scholar

Uhlenbeck, G. E. 1955. The statistical mechanics of non-equilibrium phenomena. Lecture Notes.Google Scholar

Vallée, O., and Soares, M. 2004. Airy Functions and Applications to Physics. Singapore: World Scientific.Google Scholar

van Saarloos, W. 2003. Front propagation into unstable states. Physics Reports, 386(2–6), 29–222.Google Scholar

Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., and Shochet, O. 1995. Novel type of phase transition in a system of self-driven particles. Physical Review Letters, 75(6), 1226.Google Scholar

Vicsek, T., and Zafeiris, A. 2012. Collective motion. Physics Reports, 517, 71–140.Google Scholar

Viswanathan, G. M., Buldyrev, S. V., Havlin, S., Da Luz, M. G. E., Raposo, E. P., and Stanley, H. E. 1999. Optimizing the success of random searches. Nature, 401(6756), 911.Google Scholar

Viswanathan, G. M., da Luz, M. G. E., Raposo, E. P., and Stanley, H. E. 2011. The Physics of Foraging: An Introduction to Random Searches and Biological Encounters. Cambridge, UK: Cambridge University Press.Google Scholar

Volkov, I., Banavar, J. R., He, F., Hubbell, S. P., and Maritan, A. 2005. Density dependence explains tree species abundance and diversity in tropical forests. Nature, 438(7068), 658.Google Scholar

Volpert, V., and Petrovskii, S. 2009. Reaction–diffusion waves in biology. Physics of Life Reviews, 6(4), 267–310.Google Scholar

Volterra, V. 1927. Variazioni e fluttuazioni del numero d’individui in specie animali conviventi. C. Ferrari.Google Scholar

Wade, R. C., Gabdoulline, R. R., Lüdemann, S. K., and Lounnas, V. 1998. Electrostatic steering and ionic tethering in enzyme–ligand binding: Insights from simulations. Proceedings of the National Academy of Sciences USA, 95(11), 5942–5949.Google Scholar

Wakita, J.-I., Komatsu, K., Nakahara, A., Matsuyama, T., and Matsushita, M. 1994. Experimental investigation on the validity of population dynamics approach to bacterial colony formation. Journal of the Physical Society of Japan, 63(3), 1205–1211.Google Scholar

Wang, C., Horby, P. W., Hayden, F. G., and Gao, G. F. 2020. A novel coronavirus outbreak of global health concern. Lancet, 395(10223), 470–473.Google Scholar

Wang, M. D., Yin, H., Landick, R., Gelles, J., and Block, S. M. 1997. Stretching DNA with optical tweezers. Biophysical Journal, 72(3), 1335.Google Scholar

Wang, Z., Alsayed, A. M., Yodh, A. G., and Han, Y. 2010. Two-dimensional freezing criteria for crystallizing colloidal monolayers. Journal of Chemical Physics, 132(15), 154501.Google Scholar

Ward, A. J. W., Sumpter, D. J. T., Couzin, I. D., Hart, P. J. B., and Krause, J. 2008. Quorum decision-making facilitates information transfer in fish shoals. Proceedings of the National Academy of Sciences USA, 105(19), 6948–6953.Google Scholar

Waser, P. M. 1981. Sociality or territorial defense? The influence of resource renewal. Behavioral Ecology and Sociobiology, 8, 231–237.Google Scholar

Watts, D. J. 2000. Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton, NJ: Princeton University Press.Google Scholar

Wax, N. 1954. Selected Papers on Noise and Stochastic Processes. New York: Courier Dover Publications.Google Scholar

Weber, H., Marx, D., and Binder, K. 1995. Melting transition in two dimensions: a finite-size scaling analysis of bond-orientational order in hard disks. Physical Review B, 51(20), 14636–14651.Google Scholar

West, B. J., Bologna, M., and Grigolini, P. 2003. Physics of Fractal Operators. New York: Springer.Google Scholar

West, G. B., Brown, J. H., and Enquist, B. J. 1997. A general model for the origin of allometric scaling laws in biology. Science, 276(5309), 122–126.Google Scholar

Wilson, E. O. 2000. Sociobiology: The New Synthesis. 25th ed. Cambridge, MA: Harvard University Press.Google Scholar

Wolff, J. O. 1993. Why are female small mammals territorial? Oikos, 68, 364–370.Google Scholar

Wolff, J. O. 1997. Population regulation in mammals: an evolutionary perspective. Journal of Animal Ecology, 66, 1–13.Google Scholar

Wolff, J. O., and Peterson, J. A. 1998. An offspring-defense hypothesis for territoriality in female mammals. Ethology Ecology and Evolution, 10, 227–239.Google Scholar

Yates, T. L., Mills, J. N., Parmenter, C. A., Ksiazek, T. G., Parmenter, R. R., Vande Castle, J, Calisher, R., Nichol, C. H., Abbott, S. T., Young, K. D., Morrison, J. C., Beaty, M. L., Dunnum, B. J., Baker, J. L., Salazar-Bravo, R. J., Peters, J., C. J. 2002. The ecology and evolutionary history of an emergent disease: Hantavirus pulmonary syndrome. BioScience, 52(11), 989–998.Google Scholar

Young, A. P. 1979. Melting and the vector Coulomb gas in two dimensions. Physical Review B, 19(4), 1855–1866.Google Scholar

Zaburdaev, V., Denisov, S., and Klafter, J. 2015. Lévy walks. Reviews of Modern Physics, 87(2), 483.Google Scholar

Zumaya, M., Larralde, H., and Aldana, M. 2018. Delay in the dispersal of flocks moving in unbounded space using long-range interactions. Scientific Reports, 8(1), 1–9.Google Scholar

Zwanzig, R. 1964. On the identity of three generalized master equations. Physica, 30(6), 1109–1123.Google Scholar

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