Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T23:00:50.526Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling insurgent attack dynamics across geographic scales and in cyberspace†

Published online by Cambridge University Press:  21 July 2015

N. F. JOHNSON ,
D. E. JOHNSON  and
E. M. RESTREPO
N. F. JOHNSON
Affiliation:
Department of Physics, University of Miami, Coral Gables, FL 33124, USA email: [email protected]
D. E. JOHNSON
Affiliation:
Department of Government, Harvard University, Cambridge, MA 02138, USA email: [email protected]
E. M. RESTREPO
Affiliation:
Department of Geography, University of Miami, Coral Gables, FL 33124, USA email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We discuss the emergence of common mathematical patterns governing the timing and severity of insurgent and terrorist attacks, across geographic scales and including cyberspace. We present mathematical models that provide a generative explanation of these patterns. Despite wide variations in the underlying settings and circumstances, the ubiquity of these patterns suggests there is a common way in which groups of humans fight each other. Our empirical findings follow from the analysis of myriad state-of-the-art datasets with resolution at the level of individual attacks, while our mathematical modelling involves numerical and analytical solutions of fission–fusion dynamics together with progress curve analysis.

Keywords

Modelling and interdisciplinarityBehavioural and social sciencesApplications in sciences
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 3: Mathematical Modelling of Crime and Security , June 2016 , pp. 357 - 376
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

NFJ gratefully acknowledges a grant from the Office of Naval Research (ONR): N000141110451.

References

[1]Richardson, L. F. (1960) Statistics of deadly quarrels (Boxwood, Pittsburgh).Google Scholar
[2]Lanchester, F. W. (1956) Mathematics in warfare. In: Newman, J. R., Simon & Schuster (editors), The World of Mathematics, Vol. 4, pp. 2138.Google Scholar
[3]Ispolatov, I., Krapivsky, P. L. & Redner, S. (1996) War: The dynamics of vicious civilizations. Phys. Rev. E 54, 1274.Google Scholar
[4]D'Hulst, R. & Rodgers, G. J. (2000) Exact solution of a model for crowding and information transmission in financial markets. Int. J. Theor. Appl. Finance 3, 609.Google Scholar
[5]Eguiluz, V. & Zimmermann, M. (2000) Transmission of information and herd behavior: An application to financial markets. Phys. Rev. Lett. 85, 5659.Google Scholar
[6]Galam, S. (2002) Minority opinion spreading in random geometry. Eur. Phys. J. B 25, 403.Google Scholar
[7]Clauset, A., Young, M. & Gleditsch, K. S. (2007) On the Frequency of Severe Terrorist Events. J. Conflict Resolution 51, 1.Google Scholar
[8]Clauset, A. & Gleditsch, K. S. (2011) The developmental dynamics of terrorist organizations. Preprint, http://arxiv.org/abs/0906.3287 PLOS ONE 7(11): e48633 (2012).Google Scholar
[9]Galam, S., & Mauger, A. (2003) On reducing terrorism power: A hint from physics. Physica A 323, 695.Google Scholar
[10]Lim, M., Metzler, R. & Bar-Yam, Y. (2007) Global pattern formation and ethnic/cultural violence. Science 317, 1540.CrossRefGoogle ScholarPubMed
[11]Couzin, I. D. (2006) Behavioral ecology: Social organization in fission–fusion societies. Curr. Biol. 16, R170.CrossRefGoogle ScholarPubMed
[12]Braithwaite, A. & Johnson, S. D. (2012) Space-time modeling of insurgency and counterinsurgency in Iraq. J. Quant. Criminology 28, 31.Google Scholar
[13]Bowers, K. J. & Johnson, S. D. (2014) Crime mapping as a tool for security and crime prevention. In: The Handbook of Security, Palgrave Macmillan, London.Google Scholar
[14]Woodworth, J. T., Mohler, G. O., Bertozzi, A. L. & Brantingham, P. J. (2014) Nonlocal crime density estimation incorporating housing information. Phil. Trans. Roy. Soc. A 372, 20130403.Google Scholar
[15]Zipkin, J., Short, M. B., Bertozzi, A. L. (2014) Cops on the dots in a mathematical model of urban crime and police response. Discrete Continuous Dyn. Syst. B 19, 1479.Google Scholar
[16]Gambetta, D. (2009) Codes of the Underworld: How Criminals Communicate, Princeton University Press. Princeton, NJ, USA.Google Scholar
[17]Robb, J. (2007) Brave New War: The Next Stage of Terrorism and the End of Globalization, Wiley. Hoboken, NJ, USA.Google Scholar
[18]Kenney, M. (2007) From Pablo to Osama: Trafficking and Terrorist Networks, Government Bureaucracies, and Competitive Adaptation, Pennsylvania State University Press. University Park, PA, USA.Google Scholar
[19]Kilcullen, D. (2009) The Accidental Guerrilla: Fighting Small Wars in the Midst of a Big One, Oxford University Press, Oxford.Google Scholar
[20]Kalyvas, S. N. (2006) The Logic of Violence in Civil War, Cambridge University Press, Cambridge.Google Scholar
[21]Buhaug, H., Cederman, L. E. & Gleditsch, K. S. (2013) Grievances and Inequality in Civil Wars, Cambridge University Press, Cambridge.Google Scholar
[22]Johnson, D. D. P. & Tierney, D. (2011) The Rubicon theory of war: How the path to conflict reaches the point of no return. Int. Secur. 36, 7.CrossRefGoogle Scholar
[23]Bohannon, J. (2011) Counting the dead in Afghanistan. Science. 331, 1256.Google Scholar
[24]Caro, T. (2005) Antipredator Defenses in Birds and Mammals, University of Chicago Press. Chicago, IL, USA.Google Scholar
[25]Horgan, J. (2005) Psychology of Terrorism, Routledge, Abingdon.Google Scholar
[26]McCulloh, I. A., Carley, K. M. & Webb, M. (2007) Social network monitoring of Al-Qaeda. Netw. Sci. 1, 25.Google Scholar
[27]Johnson, N., Jefferies, P. & Hui, P. (2003) Financial Market Complexity, Oxford University Press, Oxford.Google Scholar
[28]Johnson, N., Carran, S., Botner, J., Fontaine, K., Laxague, N., Nuetzel, P., Turnley, J. & Tivnan, B. (2011) Pattern in escalations in insurgent and terrorist activity. Science 333, 81.CrossRefGoogle ScholarPubMed
[29]Bohorquez, J. C., Gourley, S., Dixon, A., Spagat, M. & Johnson, N. (2009) Common ecology quantifies human insurgency. Nature 462, 911.Google Scholar
[30]Johnson, N. F., Manrique, P. & Hui, P. M. (2013) Heterogeneity in conflict dynamics. J. Stat. Phys. DOI 10.1007/s10955-013-0706-z. Vol 151, p. 395 (2013).Google Scholar
[31]For full details, see http://mathematicsofwar.com/Google Scholar
[32]Zhao, Z., Bohorquez, J. C., Dixon, A. & Johnson, N. F. (2009) Anomalously slow attrition times for asymmetric populations with internal group dynamics. Phys. Rev. Lett. 103, 148701.Google Scholar
[33]Ruszczycki, B., Zhao, Z., Burnett, B. & Johnson, N. F. (2009) Relating the microscopic rules in coalescence-fragmentation models to the cluster-size distribution. Eur. Phys. J. 72, 289.Google Scholar
[34]Johnson, N. F., Ashkenazi, J., Zhao, Z. & Quiroga, L. (2011) Equivalent dynamical complexity in a many-body quantum and collective human system. AIP Adv. 1, 012114.Google Scholar
[35]Johnson, N. F., Xu, C., Zhao, Z., Ducheneaut, N., Yee, N., Tita, G. & Hui, P. M. (2009) Human group formation in online guilds and offline gangs driven by a common team. Phys. Rev. E 79, 066117.Google Scholar
[36]Dixon, A., Zhao, Z., Bohorquez, J. C., Denney, R. & Johnson, N. (2010) Statistical physics and modern human warfare. In: Naldi, G.et al. (editors), Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences, Birkhauser, Boston, MA, p. 365.Google Scholar
[37]Zhao, Z., Kirou, A., Ruszczycki, B. & Johnson, N. F. (2009) Dynamical clustering as generator of complex system dynamics. Math. Models Methods Appl. Sci. 19, 1539.Google Scholar
[38]Zhao, Z., Calderon, J. P., Xu, C., Zhao, G., Fenn, D., Sornette, D., Crane, R., Hui, P. M. & Johnson, N. F. (2010) Effect of social group dynamics on contagion. Phys. Rev. E 81, 056107.Google Scholar
[39]Johnson, N. (2008) Mathematics, physics and crime. Policing 2, 160.Google Scholar
[40]Johnson, N. F. (November 2006) The Mother (Nature) of All Wars: Conflict, global terrorism and complexity science. APS News.Google Scholar
[41]Johnson, N. F. (2008) Complexity in human conflict. In: Helbing, D. (editor), Managing Complexity: Insights, Concepts, Applications, Springer, Berlin, p. 303.CrossRefGoogle Scholar
[42]Johnson, N., Spagat, M., Restrepo, J., Bohorquez, J., Suarez, N., Restrepo, E. & Zarama, R. (2005) From old wars to new wars and global terrorism. e-print arXiv:physics/0506213.Google Scholar
[43]Johnson, N. F., Spagat, M., Restrepo, J. A., Becerra, O., Bohorquez, J. C., Suarez, N., Restrepo, E. M. & Zarama, R. (2006) Universal patterns underlying ongoing wars and terrorism. e-print arXiv:physics/0605035.Google Scholar
[44]Bouchaud, J. P. & Potters, M. (2004) Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management, Cambridge University Press, Cambridge.Google Scholar
[45]Mantegna, R. N. & Stanley, H. E. (1995) Scaling behaviour in the dynamics of an economic index. Nature 376, 46.CrossRefGoogle Scholar
[46]Johnson, N. F., Restrepo, E. M. & Johnson, D. E. (2015) Modeling human conflict and terrorism across geographic scales. In: Gonzalves, B. (editor), Social Phenomena: From Data to Models, Springer, pp. 3–25. New York, USA.Google Scholar
[47]Johnson, N. F., Medina, P., Zhao, G., Messinger, D. S., Horgan, J., Gill, P., Bohorquez, J. C., Mattson, W., Gangi, D., Qi, H., Manrique, P., Velasquez, N., Morgenstern, A., Restrepo, E., Johnson, N., Spagat, M. & Zarama, R. (2013) Simple mathematical law benchmarks human confrontations. Sci. Rep. 3, 3463.Google Scholar
[48]Restrepo, J., Spagat, M. & Vargas, J. (2006) The severity of the colombian conflict: Cross-country datasets versus new micro data. J. Peace Res. 43, 99.Google Scholar
[49]Kappler, K. E. & Kaltenbrunner, A. (2012) The power laws of violence against women: Rescaling research and policies. PLoS ONE 7, e40289.Google Scholar
[50]Epstein, J. (1997) Nonlinear Dynamics, Mathematical Biology and Social Sciences, Addison-Wesley, Reading.Google Scholar
[51]MacKay, N. J. (2006) Lanchester combat models. Math. Today: Bull. Inst. Math. Appl. 42, 170.Google Scholar
[52]Felson, M. (2007) Crime and Nature, Sage Publications. Thousand Oaks, CA, USA.Google Scholar
[53]Hedstrom, P. & Ylikoski, P. (2010) Causal mechanisms in the social sciences. Annu. Rev. Sociol. 36, 49.Google Scholar
[54]Crossman, E. R. F. W. (1959) A theory of the acquisition of speed-skill. Ergonomics 2, 153.Google Scholar
[55]Johnson, E., Bellman, S. & Lohse, G. L. (2003) Cognitive Lock-In and the power law of practice. J. Mark. 67, 62.Google Scholar
[56]Clauset, A., Shalizi, C. & Newman, M. E. J. (2007) Power-law distributions in empirical data. SIAM Rev. 51, 661.CrossRefGoogle Scholar
[57]Asal, V. & Rethemeyer, R. K. (2008) The nature of the beast: Organizational structures and the lethality of terrorist attacks. J. Politics 70, 437.CrossRefGoogle Scholar
[58]Clauset, A. & Wiegel, F. W. (2010) A generalized aggregation-disintegration model for the frequency of severe terrorist attacks. J. Conflict Resolution 54, 179.CrossRefGoogle Scholar
[59]Humphries, D. A. & Driver, P. M. (1970) Protean defence by prey animals. Oecologia 5, 285.Google Scholar
[60]Exposing One of China's Cyber Espionage Units, Mandiant. (2013). Accessed 19 march 2013. URL: intelreport.mandiant.com/Mandiant_APT1_Report.pdfGoogle Scholar