Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-25T18:08:25.954Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics of the brain at global and microscopic scales: Neural networks and the EEG

Published online by Cambridge University Press:  04 February 2010

J. J. Wright  and
D. T. J. Liley
J. J. Wright
Affiliation:
Mental Health Research Institute, Parkville, Victoria 3052 Swinburne Center for Applied Neuroscience, Hawthorne, Victoria 3122, Melbourne, Australia Electronic mail: [email protected]
D. T. J. Liley
Affiliation:
Mental Health Research Institute, Parkville, Victoria 3052 Swinburne Center for Applied Neuroscience, Hawthorne, Victoria 3122, Melbourne, Australia Electronic mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

There is some complementarity of models for the origin of the electroencephalogram (EEG) and neural network models for information storage in brainlike systems. From the EEG models of Freeman, of Nunez, and of the authors' group we argue that the wavelike processes revealed in the EEG exhibit linear and near-equilibrium dynamics at macroscopic scale, despite extremely nonlinear – probably chaotic – dynamics at microscopic scale. Simulations of cortical neuronal interactions at global and microscopic scales are then presented. The simulations depend on anatomical and physiological estimates of synaptic densities, coupling symmetries, synaptic gain, dendritic time constants, and axonal delays. It is shown that the frequency content, wave velocities, frequency/wavenumber spectra and response to cortical activation of the electrocorticogram (ECoG) can be reproduced by a “lumped” simulation treating small cortical areas as single-function units. The corresponding cellular neural network simulation has properties that include those of attractor neural networks proposed by Amit and by Parisi. Within the simulations at both scales, sharp transitions occur between low and high cell firing rates. These transitions may form a basis for neural interactions across scale. To maintain overall cortical dynamics in the normal low firing-rate range, interactions between the cortex and the subcortical systems are required to prevent runaway global excitation. Thus, the interaction of cortex and subcortex via corticostriatal and related pathways may partly regulate global dynamics by a principle analogous to adiabatic control of artificial neural networks.

Keywords

chaosEEG simulationelectrocorticogramneocortexnetwork symmetryneurodynamics
Type
Target Article
Information
Behavioral and Brain Sciences , Volume 19 , Issue 2 , June 1996 , pp. 285 - 295
Copyright
Copyright © Cambridge University Press 1996

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.)

References

Abarbanel, H. D. I., Brown, R., Sidorowich, J. J. & Tsimring, L. S. (1993) The analysis of observed chaotic data in physical systems. Review of Modem Physics 65: 1331–92. [LI]CrossRefGoogle Scholar
Abeles, M. (1982) Local cortical circuits. In: Studies in brain Junction 6. Springer-Verlag. [RM]Google Scholar
Abeles, M., Prut, Y., Bergman, H. & Vaadia, E. (1994) Synchronization in neuronal transmission and its importance for information processing. In: Temporal coding in the brain, ed. Buzsaki, G., Llinas, R., Singer, W., Berthoz, A. & Cristen, . Springer-Verlag. [ZJK]Google Scholar
Aertsen, A. & Amdt, M. (1993) Response synchronization in the visual cortex. Current Opinion in Neurobiology 3:586–94. [HP]CrossRefGoogle ScholarPubMed
Agladze, N. N., Zhadin, M. N. & lgnatjev, D. A. (1995) Electrical activity of the rabbit isolated cerebral cortex after application of acetylcholine. Journal of Higher Nervous Activity 45:782–89 (in Russian). [MNZ]Google ScholarPubMed
Ahadin, M. N., Bakharev, B. V & Muravjova, L. I. (1977) Electrophysiological correlates of habituation and conditioning. Journal of Higher Nervous Activity 27:1173–79 (in Russian). [MNZ]Google Scholar
Alkon, D., Sanchez-Andres, J.-V, Ito, E. & Oka, K. (1992) Long-term transformation of an inhibitory into an excitatory GABAergic synaptic response. Proceedings of the National Academy of Sciences 89(24):11862–66. [HRE]CrossRefGoogle ScholarPubMed
Amari, S. (1972) Learning patterns and pattern sequences by self-organising nets of threshold elements. IEEE Transactions on Computers 21:1197–1206. [aJJW]CrossRefGoogle Scholar
Amit, D. J. (1990) Modelling brain function: The world of attractor neural networks. Cambridge University Press. [aJJW]Google Scholar
Amit, D. J. (1995) The Hebbian paradigm reintegrated. Behavioral and Brain Sciences 18:681. [DJA]CrossRefGoogle Scholar
Amit, D. J. & Brunel, N. (1995) Global spontaneous activity and local structured (learned) delay activity in cortex. Submitted. [DJA, rJJW]Google Scholar
Amit, D. J. & Tsodyks, M. V. (1990) Attractor neural networks with biological probe records. Network 1:381–405. [aJJW]CrossRefGoogle Scholar
Amit, D. J. & Tsodyks, M. V. (1991) Quantitative study of attractor neural networks retrieving at low spike rates: 2. Low rate retrieval in symmetric networks. Network 2:275–94. [ajJW]CrossRefGoogle Scholar
Aradi, I., Barna, G., Érdi, P. & Gröbler, T. (1995) Chaos and learning in the olfactory bulb. International Journal of Intelligent Systems 10:89–117. [PÉ]CrossRefGoogle Scholar
Babloyantz, A. & Lourenco, C. (1994) Computation with chaos: A paradign for cortical activity. Proceedings of the National Academy of Sciences USA 91:9027–31. [IT]CrossRefGoogle Scholar
Becker, C. J. & Freeman, W. J. (1968) Prepyriform electrical activity after loss of peripheral or central input or both. Physiology & Behavior 3:597–99. [WJF]CrossRefGoogle Scholar
Bennett, C. H. 91995) Quantum information and computation. Physics Today 48:24–30. [LI]CrossRefGoogle Scholar
Bower, J. M. & Beeman, D. (1995) The book of Genesis: Exploring realistic neural models with GEneral NEural SImulation System. TELOS/Springer-Verlag. [JJW]CrossRefGoogle Scholar
Braitenberg, V. (1978) Cell assemblies in the cerebral cortex. In: Theoretical approaches to complex systems [Lecture notes in Biomathematics, vol. 21], ed. Hcim, R. & Palm, C.. Springer-Verlag. [HP]CrossRefGoogle Scholar
Braitenberg, V. & Schuz, A. (1991) Anatomy of the cortex: Statistics and geometry. Springer-Verlag. [aJJW]CrossRefGoogle Scholar
Bressler, S. L., Coppola, R. & Nakamura, R. (1993) Episodic multiregional cortical coherence at multiple frequencies during visual task performance. Nature 366:153–56. [HRE, rJJW]CrossRefGoogle ScholarPubMed
Bressler, S. L. & Freeman, W. J. (1980) Frequency analysis of olfactory system EEC in cat, rabbit and rat. EEC and Clinical Neurophysiology 50:19–24. [WJF]CrossRefGoogle Scholar
Bullock, T. H. & McClune, M. C. (1989) Lateral coherence of the electrocorticogram: A new measure of brain synchrony. Electroencephalography and Clinical Neurophysiology 73:479–98. [THB]CrossRefGoogle ScholarPubMed
Bullock, T. H., McClune, M. C, Achimowicz, J. Z., Iragui-Madoz, V. J., Duckrow, R. B. & Spencer, S. S. (1995) EEC coherence has structure in the millimeter domain: Subdural and hippocampal recordings from epileptic patients. Electroencephalography and Clinical Neurophysiology 95:161–77. [THB]CrossRefGoogle Scholar
Bullock, T. H., McClune, M. C, Achimowicz, J. Z., Iragui-Madoz, V. J., Duckrow, R. B. & Spencer, S. S. (in press) Temporal fluctuations in coherence of brain waves. Proceedings of the National Academy of Sciences [THB]Google Scholar
Burkitt, G. (1994) Steady-state visually evoked potentials and travelling waves. PhD dissertation, Swinburne University of Technology, Melbourne, Australia. [aJJW]Google Scholar
Burns, B. D. (1958) Mammalian cerebral cortex. Williams and Wilkins. [WJF, rJJW]Google Scholar
Buzsaki, B. & Chrobak, J. J. (1995) Temporal structure in spatially organized neuronal emsembles: A role for intemeuronal networks. Current Opinion in Neurobiology 5:504–20. [EK]CrossRefGoogle Scholar
Caianiello, E. R., De Luca, A. & Ricciardi, L. M. (1967) Reverberations and control of neural networks. Kybernetik 4:10–18. [aJJW]CrossRefGoogle ScholarPubMed
Calvin, W. H. & Ojemann, G. A. (1994) Conversations with Neil's brain: The neural nature of thought and language. Addison Wesley. [HRE]Google Scholar
Case, R. (1992) The role of the frontal lobes in the regulation of cognitive development. Brain and Cognition 20:51–73. [AO]CrossRefGoogle ScholarPubMed
Chang, H. J. & Freeman, W. J. (in press) Parameter optimization in models of the olfactory system. Neural Networks. [WJF]Google Scholar
Churchland, P. S. (1986) Neurophilosophy–Toward a unified science of the mindbrain. MIT Press. [aJJW]Google Scholar
Churchland, P. S. & Sejnowski, T. J. (1994) The computational brain. MIT Press. [HRE]Google Scholar
Crick, F. (1994) The astonishing hypothesis: The scientific search for the soul. Scribners. [HRE]Google Scholar
Dehaene, S., Changeux, J. P. & Nadal, J. P. (1987) Neural networks that learn temporal sequences by selection. Proceedings of the National Academy of Science 84:2727–31. [aJJW]CrossRefGoogle ScholarPubMed
Dennett, D. C. (1991) Consciousness explained. Little, Brown. [HRE]Google Scholar
DeWitt, B. S. (1957) Dynamical theory in curved spaces: 1. A review of the classical and quantum action principles. Review of Modem Physics 29:377–97. [LI]CrossRefGoogle Scholar
Donchin, E. (1981) Suprise! … Surprise? Psychophysiology 18:493–513. [MM]CrossRefGoogle Scholar
Eckhom, R. (1994) Oscillatory and non-oscillatory synchronization in the visual cortex of cat and monkey. In: Oscillatory event-related brain dynamics ed. Pantev, C., Elbert, T. & Lutkenhoner, B.. NATO ASI Series A: life Sciences, vol. 271. Plenum. [ZJK]Google Scholar
Eckhom, R., Bauer, B., Jordan, W., Brosch, M., Kruse, W., Munk, M. & Reitboeck, H. J. (1988) Coherent oscillation: A mechanism of feature linking in visual cortex? Biological Cybernetics 60:121–30. [aJJW, HP]Google Scholar
Eeckman, F. H. & Freeman, W. J. (1991) Asymmetric sigmoid nonlinearity in the rat olfactory system. Brain Research 557:13–21. [aJJW]CrossRefGoogle ScholarPubMed
Elbert, T., Ray, W. J., Kowalik, Z. J., Skinner, J. E., Graf, K. E. & Birbaumer, N. (1994) Chaos and physiology: Deterministic chaos in excitable cell assemblies. Physiological Reviews 74:1–47. [ZJK, HP]CrossRefGoogle ScholarPubMed
Elbert, T. & Rockstroh, B. (1987) Threshold regulation: A key to the understanding of the combined dynamics of EEC and event-related potentials. Journal of Psychophysiology 4:317–33. [HP]Google Scholar
Érdi, P. (1983) Hierarchical approach to the brain. International Journal of Neuroscience 20:193–216. [PÉ]CrossRefGoogle ScholarPubMed
Érdi, P., Gröbler, T. & Toth, J. (1992) On the classification of some classification problems. International Symposium on Information Physics, Kyushu Institute of Technology, Iizuka, Fukuoka, Japan. [PÉ]Google Scholar
Farley, B. G. (1965) A neuronal network model and the “slow potentials” in electrophysiology. In: Computers in biomedical research, ed. Stacy, R. W. & Waxman, B. D.. Academic Press. [MNZ]Google Scholar
Farmer, J. D. (1982) Information dimension and the probabilistic structure of chaos. Zeitschrifi für Naturforschung 37a:1304–25. [HP]CrossRefGoogle Scholar
Freeman, W. J. (1964) A linear distributed feedback model for prepyriform cortex. Experimental Neurology 10:525–47. [aJJW]CrossRefGoogle ScholarPubMed
Freeman, W. J. (1972) Measurement of open-loop responses to electrical stimulation in olfactory bulb of cat. Journal of Neurophysiology 35:745–61. [aJJW]CrossRefGoogle ScholarPubMed
Freeman, W. J. (1975) Mass action in the nervous system. Academic Press. [aJJW, HRE, WJF, PLN]Google Scholar
Freeman, W. J. (1979) Nonlinear gain mediation of cortical stimulus response relations. Biological Cybernetics 33:237–47. [aJJW, WJF, HL]CrossRefGoogle ScholarPubMed
Freeman, W. J. (1987a) Techniques used in the search for die physiological basis of the EEC. In: Handbook of electroencephalography and clinical neurophysiology, vol. 3A, ed. Gevins, A. S. & Remond, A.. Elsevier. [aJJW]Google Scholar
Freeman, W. J. (1987b) Simulation of chaotic EEC patterns with dynamic model of the olfactory system. Biological Cybernetics 56:139–50. [aJJW]CrossRefGoogle Scholar
Freeman, W. J. (1988) Strange attractors diat govern mammalian brain dynamics shown by trajectories of electroencephalographic (EEG) potential. IEEE Transactions on Circuits and Systems 35:781–83. [aJJW]CrossRefGoogle Scholar
Freeman, W. J. (1991) Predictions on neoeortical dynamics derived from studies in paleoeortex. In: Induced rhythms of the brain, ed. Basar, E. & Bullock, T. H.. Birkhaeuser Boston Inc. [aJJW, ZJK]Google Scholar
Freeman, W. J. (1992) Tutorial in neurobiology: From single neurons to brain chaos. International Journal of Bifurcation and Chaos 2:451–82. [WJF]CrossRefGoogle Scholar
Freeman, W. J. (1994) Neural mechanisms underlying destabilization of cortex by sensory input. Physica D 75:151–64. [IT]CrossRefGoogle Scholar
Freeman, W. J. (1995a) Societies of brains: A study in the neuroscience of love and hate. Erlbaum. [HRE, WJF, IT]Google Scholar
Freeman, W. J. (1995b) Foreword. In: Chaos theory in psychology and the life sciences, ed. Robertson, R. & Combs, A.. Erlbaum. [rJJW, MM]Google Scholar
Freeman, W. J. (1995c) Chaos in the brain: Possible roles in biological intelligence. International Journal of Intelligent Systems 10:71–88. [IT]CrossRefGoogle Scholar
Freeman, W. J. & Barrie, J. M. (1994) Chaotic oscillations and the genesis of meaning in cerebral cortex. In: Temporal coding in the brain, ed. Buzsaki, C., Llinás, R., Singer, W., Berthoz, A. & Christen, Y.. Springer-Verlag. [WJF]Google Scholar
Freeman, W. J., Barrie, J. M., Lenhart, M. & Tang, R. X. (1995) Spatial phase gradients in neoeortical EECs give modal diameter of “binding” domains in perception. Society for Neuroscience Abstracts 21:1649. [WJF]Google Scholar
Freeman, W. J. & Jakubith, S. (1993) Bifurcation analysis of continuous time dynamics of oscillatory neural networks. In: Brain theory, ed. Aertson, A.. Springer-Verlag. [aJJW, ZJK]Google Scholar
Freeman, W. J. & Skarda, C. A. (1985)' Spatial EEG patterns, nonlinear dynamics and perception: The neo-Sherringtonian view. Brain Research Reviews 10:147–75. [aJJW]CrossRefGoogle Scholar
Friedrich, R., Fuchs, A. & Hakan, H. (1991) Spatio-temporal EEG patterns. In: Rhythms in physiological systems, ed. Hakan, H. & Koepshen, H. P.. Springer-Verlag. [PLN]Google Scholar
Fuchs, A., Kelso, J. A. S. & Hakan, H. (1992) Phase transitions in the human brain spatial mode dynamics. International Journal of Bifurcation and Chaos 2:917–39. [PLN]CrossRefGoogle Scholar
Gevins, A. S., Schaffer, R. E., Doyle, J. C., Cuttilo, B. A., Tannehill, R. S. & Bressler, S. L. (1983) Shadows of thought: Shifting lateralisation of human brain electrical patterns during a brief visuomotor task. Science 220:97–99. [aJJW]CrossRefGoogle ScholarPubMed
Glass, L., Kaplan, D. T. & Lewis, J. E. (1993) Tests for deterministic dynamics in real and model neural networks. In: Nonlinear dynamical analysis of the EEG, ed. Jansen, B. H. & Brandt, M. E.. World Scientific. [WSP]Google Scholar
Graham, R. (1978) Path-integral methods on nonequilibrium thermodynamics and statistics. In: Stochastic processes in nonequilibrium systems, ed. Garrido, L., Seglar, P. & Shepherd, P. J.. Springer-Verlag. [LI]Google Scholar
Grassberger, P. & Procaccia, I. (1983) Measuring die strangeness of strange attractors. Physica D 9:189–208. [MM, WSP]CrossRefGoogle Scholar
Gray, C. M., Koenig, P., Engel, K. A. & Singer, W. (1989) Oscillatory responses in cat visual cortex exhibit intereolumnar synchronisation which reflects global stimulus properties. Nature 338:334–37. [aJJW, HP]CrossRefGoogle ScholarPubMed
Gregson, R. A. M. (1992) Cognitive load as a determinant of the dimensionality of the electroencephalogram: A replication study. Biological Psychology 35:165–78. [MM]CrossRefGoogle Scholar
Grey, G. M., Koning, P., Engle, A. K. & Singer, W. (1989) Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 338:334–37. [PLN]CrossRefGoogle Scholar
Griniasty, M., Tsodyks, M. V. & Amit, D. J. (1993) Conversion of temporal correlations between stimuli to spatial correlations between attractors. Neural Computation 5:1–17. [aJJW]CrossRefGoogle Scholar
Haken, H. (1977) Synergistics: An introduction. Springer-Verlag. [PÈ]Google Scholar
Hopfield, J. J. (1982) Neural networks and physical systems with emergent collective computational abilities. Proceedings of National Academy of Sciences 79:2554–58. [aJJW]CrossRefGoogle ScholarPubMed
Hopfield, J. J. (1984) Neurones with graded response have collective computational properties like those of two state neurones. Proceedings of National Academy of Science 81:3088–92. [aJJW]CrossRefGoogle Scholar
Hopfield, J. J. & Tank, D. W. (1986) Computing with neural circuits: A model. Science 233:625–33. [aJJW]CrossRefGoogle ScholarPubMed
Houk, J. (1974) Feedback control of muscle: A synthesis of the peripheral mechanisms. In: Medical physiology, 13th ed., ed. Mountcastle, V. B.. Mosby. [WJF]Google Scholar
Ikeda, K., Otsuka, K. & Matsumoto, K. (1989) Maxwell-Bloch turbulence. Progress of Theoretical Physics [Suppl.] 99:295–313. [IT]CrossRefGoogle Scholar
Ingber, L. (1981) Towards a unified brain theory. Journal of Social and Biological Structures 4:211–24. [LI]CrossRefGoogle Scholar
Ingber, L. (1982) Statistical mechanics of neocortical interactions: 1. Basic formulation. Physica D 5:83–107. [LI]CrossRefGoogle Scholar
Ingber, L. (1983) Statistical mechanics of neocortical interactions: Dynamics of synaptic modification. Physical Review A 28:395–416. [LI, PLN]CrossRefGoogle Scholar
Ingber, L. (1984a) Path-integral Riemannian contributions to nuclear Schrödinger equation. Physical Review D 29:1171–74. [LI]Google Scholar
Ingber, L. (1984b) Statistical mechanics of neocortical interactions: Derivation of shortterm-memory capacity. Physical Review A 29:3346–58. [LI]CrossRefGoogle Scholar
Ingber, L. (1984c) Statistical mechanics of nonlinear nonequilibrium financial markets. Mathematical Modelling 5:343–61. [LI]CrossRefGoogle Scholar
Ingber, L. (1985) Statistical mechanics of neocortical interactions: Stability and duration of the 7 ± 2 rule of short-term-memory capacity. Physical Review A 31:1183–86. [LI]CrossRefGoogle Scholar
Ingber, L. (1989) Very fast simulated re-annealing. Mathematical and Computer Modelling 12:967–73. [LI]CrossRefGoogle Scholar
Ingber, L. (1990) Statistical mechanical aids to calculating term structure models. Physical Review A 42:7057–64. [LI]CrossRefGoogle ScholarPubMed
Ingber, L. (1991) Statistical mechanics of neoeortical interactions: A scaling paradigm applied to electroencephalography. Physical Review A 44:4017–60. [LI]CrossRefGoogle ScholarPubMed
Ingber, L. (1992) Generic mesoscopic neural networks based on statistical mechanics of neocortical interactions. Physical Review A 45:2183–R2186. [LI]CrossRefGoogle ScholarPubMed
Ingber, L. (1993) Adaptive simulated annealing (ASA) [ftp.alumni.caltech.edu:/pub/ingber/ASA-shar, ASA-shar.Z, ASA.tar.Z, ASA.tar.gz, ASA.zip]. Lester Ingber Research. [LI]Google Scholar
Ingber, L. (1994) Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory. Physical Review E 49:4652–64. [LI]CrossRefGoogle ScholarPubMed
Ingber, L. (1995a) Statistical mechanics of multiple scales of neocortical interactions. In: Neocortical dynamics and human EEG rhythms, ed. Nunez, P. L.. Oxford University Press. [LI, PLN]Google Scholar
Ingber, L. (1995b) Statistical mechanics of neocortical interactions (SMN1). SMNI Lecture Plates. Lester Ingber Research. [LI]Google Scholar
Ingber, L. (1996a) Adaptive simulated annealing of canonical momenta indicators of financial market. Submitted. [LI]CrossRefGoogle Scholar
Ingber, L. (1996b) Trading markets with canonical momenta and adaptive simulated annealing. Submitted. [LI]Google Scholar
Ingber, L. (in press a) Statistical mechanics of neocortical interactions: Constraints on 40 Hz models of short-term memory. Physical Review E [LI]Google Scholar
Ingber, L. (in press b) Statistical mechanics of nonlinear nonequilibrium financial markets: Applications to optimized trading. Mathematical and Computer Modelling. [LI]Google Scholar
Ingber, L. (in press c) Statistical mechanics of neocortical interactions: Statistical mechanics of neoeortical interactions: Multiple scales of EEG. Electroencephalography and Clinical Neurophysiology. [LI]Google Scholar
Ingber, L. & Nunez, P. L. (1990) Multiple scales of statistical physics of neocortex: Application to electroencephalogaphy. Mathematical and Computer Modelling 13:83–95. [aJJW, LI]CrossRefGoogle Scholar
Ingber, L. & Nunez, P. L. (1995) Statistical mechanics of neocortical interactions: High resolution pathintegral calculation of short-term memory. Physical Review E 51:5074–83. [LI, PLN]CrossRefGoogle ScholarPubMed
Ingber, L., Srinivasan, R. & Nunez, P. L. (in press) Path-integral evolution of chaos embedded in noise: Duffing neocortical analog. Mathematical and Computer Modelling. [LI]Google Scholar
Joliot, M., Ribary, U. & Llinás, R. (1994) Human oscillatory brain activity near 40 Hz coexists with cognitive temporal binding. Proceedings of the National Academy of Sciences USA 91:11748–51. [EK]CrossRefGoogle ScholarPubMed
Kaneko, K. (1990a) Globally coupled chaos violates the law of large numbers. Physical Review Letters 65:1391–94. [aJJW, ZJK, IT]CrossRefGoogle ScholarPubMed
Kaneko, K. (1990b) Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements. Physica D 41:137–72. [IT]CrossRefGoogle Scholar
Kaneko, K. (1992) Mean field fluctuation in network of chaotic elements. Physica D 55:368–84. [aJJW, IT]CrossRefGoogle Scholar
Kaplan, D. & Glass, L. (1992) Direct test for determinism in a time series. Physical Review Letters 68:427–30. [ZJK, WSP]CrossRefGoogle Scholar
Kay, L., Shimoide, K. & Freeman, W. J. (1995) Comparison of EEG time series from rat olfactory system with model composed of nonlinear coupled oscillators. International Journal of Bifurcation and Chaos 5:849–58. [IT]CrossRefGoogle Scholar
Kerszberg, M., Dehaene, S. & Changeux, J. P. (1992) Stabilization of complex input-output functions in neural clusters formed by synapse selection. Neural Networks 5:403–13. [AO]CrossRefGoogle Scholar
Kishida, K. (1982) Physical Langevin model and the time-series model in systems far from equilibrium. Physical Review A 25:496–507. [LI]CrossRefGoogle Scholar
Kishida, K. (1984) Equivalent random force and time-series model in systems far from equilibrium. Jounal of Mathematical Physics 25:1308–13. [LI]CrossRefGoogle Scholar
Kleinfeld, D. (1986) Sequential state generation by model neural networks. Proceedings of National Academy of Sciences 83:9469–73. [rJJW]CrossRefGoogle ScholarPubMed
Kowalik, Z. J., Elbert, T. & Hoke, M. (1993) Mapping brain functions: The largest Lyapunov exponents derived from multi-channel magnetoencephalography. In: Nonlinear dynamic analysis of the EEG, & Jansen, B. H. & Brandt, M. E.. Singapore: World Scientific. [ZJK]Google Scholar
Krakowska, D., Waleszczyk, W., Bekisz, M. & Wrobel, A. (1995) General 20 Hz synchronization within cortico-thalamic division of the cat's visual system shifts to specific pattern during visual attention. European Journal of Neuroscience [Suppl.] 8:38. [ZJK]Google Scholar
Langouche, F., Roekaerts, D. & Tirapegui, E. (1982) Functional integration and semiclassical expansions. Reidel. [LI]CrossRefGoogle Scholar
Langton, C. G., Taylor, C., Farmer, J. D., & Rassmussen, S., Eds. (1992) Artificial life 2: Santa Fe Institute studies in the sciences of complexity [Proceedings vol. 10]. Addison-Wesley. [arJJW]Google Scholar
Liley, D. T. J. (1995) Models of electrocortical dynamics. PhD thesis, University of Auckland, New Zealand. [rJJW]Google Scholar
liley, D. T. J. & Wright, J. J. (1994) Intracortical connectivity of pyramidal and stellate cells: Estimates of synaptic densities and coupling symmetry. Network: Computation in Neural Systems 5:175–89. [arJJW]CrossRefGoogle Scholar
Liljenström, H. (1991) Modeling the dynamics of olfactory cortex using simplified network units and relistic architecture. International Journal Systems 2:1–15. [HL]Google Scholar
Liljenström, H. & Hasselmo, M. E. (1995) Cholinergic modulation of cortical oscinamics. Journal of Neurophysiology 74:288–97. [HL]CrossRefGoogle Scholar
Liljenström, H. & Wu, X. (1995) Noise-enhanced performance in a cortical associative memory model. International Systems 6:19–29. [HL]Google Scholar
Lisman, J. E. & Idiart, M. A. P. (1995) Storage of 7 ± 2 short-term memories in oscillatory subcycles. Science 267:1512–15. [LI]CrossRefGoogle Scholar
Little, W. A. & Shaw, G. L. (1975) A statistical theory of short and long term memory. Behavioural Biology 14:115–33. [aJJW]CrossRefGoogle ScholarPubMed
Llinás, R. & Ribary, U. (1993) Coherent 40-Hz oscillation characterized dream state in humans. Proceedings of the National Academy of Sciences USA 90:2078–81. [EK]CrossRefGoogle ScholarPubMed
Lopes da Silva, F. H. & Storm van Leeuwen, W. (1978) The cortical alpha rhythm in dog: The depth and surface profile of phase. In: Architectonics of the cerebral cortex, ed. Brazier, M. A. B. & Petsche, H.. Raven. [aJJW]Google Scholar
Lopes da Silva, F. H., van Rotterdam, A., Barts, P., van Heusden, E. & Burr., B. (1976) Models of neuronal populations, the basic mechanisms of rhythmicity. Progress in Brain Research 45:282–308. [MNZ]Google ScholarPubMed
Lutzenberger, W., Elbert, T., Ray, W. J. & Birbaumer, N. (1993) The scalp distribution of the fractal dimension of the EEG and its variation with mental tasks. Brain Topography 5:27–34. [MM]CrossRefGoogle Scholar
Matsumoto, K. & Tsuda, I. 91983) Noise-induced order. Journal of Statistical Physics 31:87–106. [IT]CrossRefGoogle Scholar
McCulloch, W. S. & Pitts, W. H. (1943) A logical calculus of ideas immanent in nervous activity. Bulletin of Mathematical Biophysics 5:115–33. [HRE]CrossRefGoogle Scholar
Menon, V., Freeman, W. J., Cutillo, B. A., Desmond, J. E., Ward, M. F., Bressler, S. L., Laxer, K. D., Barbaro, N. M. & Gevins, A. S. (in press) Spatio-temporal correlations in human gamma band electroeorticograms. Electroencephalography and Clincal Neurophysiology. [WJF]Google Scholar
Miller, G. A. (1956) The magical number seven, plus or minus two. Psychology Review 63:81–97. [LI]CrossRefGoogle ScholarPubMed
Miller, K. D., Keller, J. D. & Stryker, M. P. (1989) Ocular dominance column development: Analysis and simulation. Science 245:605–15. [AO]CrossRefGoogle ScholarPubMed
Miller, R. (1975) Distribution and properties of commissural and other neurons in cat sensorimotor cortex. Journal of Comparative Neurology 164:361–74. [RM]CrossRefGoogle ScholarPubMed
Miller, R. (1989) Cortico-hippocampal interplay: Self-organizing phase-locked loops for indexing memory. Psychobiology 17:115–28. [RM]CrossRefGoogle Scholar
Miller, R. (1993) An interpretation, based on cell assembly theory, of the psychological impairments following lesions of the the hippocampus and related structures. In:The memory system of the brain: Advanced series in neuroscience, vol. 4. Singapore: World Scientific. [RM]Google Scholar
Miller, R. (1994) What is the contribution of axonal conduction delay to temporal structure in brain dynamics? In:Oscillatory event-related brain dynamics [NATO ASI Series, vol. 271], ed. Pantev, C., Elbert, T. & Lutkenhoner, B.. Plenum. [RM]Google Scholar
Miller, R. (in press) Axonal conduction time and human cerebral laterality: A psychobiological theory. Gordon and Breach. [RM]CrossRefGoogle Scholar
Minsky, M. (1993) Book review: Allen Newell, Unified theory of cognition. Artificial Intelligence 59:343–54. [EK, rJJW]Google Scholar
Miyashita, Y. (1988) Neuronal correlate of visual associative long-term memory in the primate temporal cortex. Nature 335:817–20. [aJJW]CrossRefGoogle ScholarPubMed
Miyashita, Y. & Chang, H. S. (1988) Neural correlate of pictorial short-term memory in the primate temporal cortex. Nature 331:68–70. [aJJW]CrossRefGoogle Scholar
Molnár, M. (1994) On the origin of the P3 event-related potential component. International Journal of Psychophysiology 17:129–44. [MM]CrossRefGoogle ScholarPubMed
Molnár, M. & Skinner, J. E. (1992) Low-dimensional chaos in event-related brain potentials. International Journal of Neuroscience 66:263–76. [MM]Google ScholarPubMed
Molnár, M., Skinner, J. E., Csépe, V., Winkler, I. & Karmos, G. (1995) Correlation dimension changes accompanying the occurrence of the msimatch-negativity and the P3 event-related potential component. Electroencephalography and Clinical Neurophysiology 95:118–26. [MM]CrossRefGoogle ScholarPubMed
Mühlnickel, W., Rendtorff, N., Kowalik, Z. J., Rockstroh, B., Miltner, W. & Elbert, T. (1994) Testing the determinism of EEG and MEG. lntegrative Physiological and Behavioral Science 29:260–67. [ZJK]Google ScholarPubMed
Nadal, J. P., Toulouse, G., Changeux, J. P. & Dehaene, S. (1986) Europhysics Letters 1(10):535–42. [aJJW]CrossRefGoogle Scholar
Nebenzahl, I. (1987) Recall of associated memories. Journal of Mathematical Biology 25:511–19. [aJJW]CrossRefGoogle ScholarPubMed
Nicolis, G. & Prigogine, I. (1977) Self-organization in nonequilibrium systems. Wiley-Interscience. [PÉ, IT]Google Scholar
Nunez, P. L. (1989a) Generation of human EEG by a combination of long and short range neocortical interactions. Brain Topography 1:199–215. [aJJW]CrossRefGoogle ScholarPubMed
Nunez, P. L. (1989b) Towards a physics of neocortex. In: Advanced methods of physiological systems modelling, vol. 2., ed. Marmarelis, V. Z.. Plenum. [PLN]Google Scholar
Nunez, P. L. (1995) Neocortical dynamics and human EEG rhythms. Oxford University Press. [aJJW, WJF, LI, PLN]Google Scholar
Nunez, P. L., Ed. (1981) Electric fields of the brain: The neurophysics of EEG. Oxford University Press. [aJJW, PLN]Google Scholar
Nunez, P. L., Silberstein, R. B., Cadusch, P. J., Wijesinghe, R. S., Westdorp, A. F. & Srinivasan, R. (1994) A theoretical and experimental study of high-resolution EEG based on surface Laplacians and cortical imaging. Electrocncephalography and Clinical Neurophysiology 90:40–57. [PLN]CrossRefGoogle ScholarPubMed
Nunez, P. L. & Srinivasan, R. (1993) Implications of recording strategy for estimates of neocortical dynamics with electroencephalography. Chaos 3:257–66. [aJJW]CrossRefGoogle ScholarPubMed
Oliver, A., Johnson, M. H. & Shrager, J. (1995) The emergence of hierarchical clustered representations in a Hebbian neural network model. Submitted. [AO]CrossRefGoogle Scholar
Palus, M. (1994) Nonlinearity in normal human EEG: Cycles and randomness not chaos [Santa Fe Institute publication no. 94–10–054]. Santa Fe Institute. [WSP]Google Scholar
Parisi, G. (1986a) A memory which forgets. Journal of Physics 19:L617–L620. [aJJW]Google Scholar
Parisi, G. (1986b) Asymmetric neural networks and the process of learning. Journal of Physics 19:L675–L680. [aJJW]Google Scholar
Penrose, R. (1989) The emperor's new mind. Oxford University Press. [HRE]CrossRefGoogle Scholar
Peretto, P. & Niez, J. J. (1986) Collective properties of neuronal networks. In: Disordered systems and biological organisation, ed. Bienenstock, E., Fogelman-Soulie, F. & Weisbuch, G.. Springer-Verlag. [aJJW]Google Scholar
Pfurtscheller, G. & Cooper, R. (1975) Frequency dependence of the transmission of the EEG from cortex to scalp. Electroencephalography and Clinical Neurophysiology 38:93–96. [PLN]CrossRefGoogle Scholar
picton, T. W. & Hillyard, S. A. (1988) Endogenous event related potentials. In: EEG handbook, ed. Picton, T. W.. Elsevier. [aJJW]Google Scholar
Pijn, J. P., van Neerven, J., Noest, A.& Lopes da Silva, F. H. 91991) Chaos or noise in EEG signals; dependence on state and brain site. Electroencephalography and Clincal Neurophysiology 79:371–81. [WSP]CrossRefGoogle Scholar
Pritchard, W. S., Duke, D. W. & Krieble, K. K. (1995) Dimensional analysis of resting human EEG: 2. Surrogate-data testing indicates nonlinearity but now low-dimensional chaos. Psychophysiology 32:486–91. [ZJK, WSP]CrossRefGoogle Scholar
Pritchard, W. S., Krieble, K. K. & Duke, D. W. (1995b) No effect of cigarette smoking on electroencephalographic nonlinearity. Psychopharatnacology 199:349–51. [WSP]CrossRefGoogle Scholar
Rapp, P. E., Albano, A. M., Schinah, T. I. & Farwell, L. A. (1993) Filtered noise can mimic low dimensional chaotic attractors. Physical Review E 47:2289–97. [LI]CrossRefGoogle ScholarPubMed
Rapp, P. E., Bashore, T. R., Martineire, J. M., Albano, A. M., Zimmerrman, I. D. & Mees, A. I. (1989) Dynamics of brain electrical activity. Brain Topography 2:99–118. [MM]CrossRefGoogle ScholarPubMed
Ruelle, D. (1994) Physics Today 47:24–30. [aJJW]CrossRefGoogle Scholar
Ruppeiner, G. (1995) Riemannian geometry in thermodynamic fluctuation theory. Review of Modern Physics 67:605–59. [LI]CrossRefGoogle Scholar
Sakai, K. & Miyashita, Y. (1991) Neural organisation for the long-term memory of paired associates. Nature 354:152–55. [aJJW]CrossRefGoogle ScholarPubMed
Schiff, J. S., Jerger, K., Duong, D. H., Chang, T., Spano, M. L. & Ditto, W. L. (1994) Controlling chaos in the brain. Nature 370:615–20. [aJJW]CrossRefGoogle ScholarPubMed
Schuz, A. (1994) Patchiness as a means to get a message across. Trends in Neuroscience 17:365. [RMJ]CrossRefGoogle ScholarPubMed
Shepherd, G. M. (1994) Neurobiology, 3d ed.Oxford University Press. [HRE]Google Scholar
Sholl, D. A. (1953) Dendritic organization in the neurones of the visual and motor cortices of the cat. Journal of Anatomy 87:387–407. [aJJW]Google ScholarPubMed
Silberstein, R. B. (1994) Neuromodulation of neocortical dynamics. In: Neocortical dynamics and human EEG rhythms, ed. Nunez, P. L.. Oxford University Press. [aJJW]Google Scholar
Silberstein, R. B. (1995) Neuromodulation of neocortical dynamics. In: Neocortical dynamics and human EEG rhythms, ed. Nunez, P. L.. Oxford University Press. [PLN]Google Scholar
Singer, W. (1994) Putative functions of temporal correlations in neocortical processing. In: Large-scale neuronal theories of the brain, ed. Koch, C.& Davis, J. L.. MIT Press. [rJJW]Google Scholar
Skarda, C. A. & Freeman, W. J. (1987) How brains make chaos in order to make sense of the world. Behavioral and Brain Sciences 10:161–95. [MM]CrossRefGoogle Scholar
Skinner, J. E., Molnár, M. & Tomberg, C. (1994) The point correlation dimension: Performance with nonstationaiy surrogate data and noise. lntegrative Physiological and Behavior Science 29:217–34. [MM]CrossRefGoogle ScholarPubMed
Skinner, J. E., Molnár, M., Vybiral, T. & Mitra, M. (1992) Application of chaos theory to biology and medicine. lntegrative Physiological and Behavioral Science 27:39–53. [MM]CrossRefGoogle ScholarPubMed
Steriade, M., Gloor, P., Llinas, R. R., Lopes da Silva, F. H. & Mesulam, M. M. (1990) Basic mechanisms of cerebral rhythmic activities. Electroencephalography and Clinical Neurophysiology 76:481–508. [arJJW]CrossRefGoogle ScholarPubMed
Stewart, M. & Fox, S. E. (1990) Do septal neurons pace the hippocampal theta rhythm? TINS 13:163–68. [EK]Google ScholarPubMed
Stryker, M. P. (1989) Is grandmother an oscillation? Nature 338:297–98. [aJJW]CrossRefGoogle ScholarPubMed
Swadlow, H. A. (1994) Efferent neurons and suspected interneurons in motor cortex of the awake rabbit: Axonal properties, sensory receptive fields and subthreshold synaptic inputs. Journal of Neurophysiology 71:437–53. [RM]CrossRefGoogle ScholarPubMed
Thatcher, R. W., Krause, P. J. & Hrybyk, M. (1986) Cortico-cortical associations and EEG coherence: A two-compartmental model. Electroencephalography and Clinical Neurophysiology 64:123–43. [aJJW, RM]CrossRefGoogle ScholarPubMed
Theiler, J., Eubank, S., Longtin, A., Galdrikian, B. & Farmer, J. D. (1992) Testing for nonlinearity in time series: The method of surrogate data. Physica D 58:77–94. [WSP]CrossRefGoogle Scholar
Tovee, M. J. & Rolls, E. T. (1992) Oscillatory activity is not evident in the primate temporal visual cortex. Neuroreport 3:369–72. [aJJW]CrossRefGoogle Scholar
Truesdell, C. (1969) Rational thermodynamics. McGraw-Hill. [PÉ]Google Scholar
Tsuda, I. (1991) Chaotic neural networks and thesaurus. In: Neurocomputers and attention: I. Neurobiology, synchronization and chaos, ed. Holden, A.V. & Krukov, V. I.. Manchester University. [IT]Google Scholar
Tsuda, I. (1992) Dynamic link of memory-chaotic memory maps in non-equilibrium neural networks. Neural Networks 5:313–26. [aJJW]CrossRefGoogle Scholar
Tsuda, I. (1994) Can stochastic renewal of maps be a model for cerebral cortex? Physica D 75:165–178. [aJJW]CrossRefGoogle Scholar
Tsuda, I., Koemer, E. & Shimuzu, H. (1987) Memory dynamics in asynchronous neural networks. Progress in Theoretical Physics 78:51–71. [aJJW, IT]CrossRefGoogle Scholar
Tsuda, I. & Matsumoto, K. (1984) Noise-induced order: Complexity theoretical digression. In: Chaos and statistical methods, ed. Kuramoto, Y.. Springer-Verlag. [IT]Google Scholar
Uttley, A. M. (1956) The probability of neural connexions. Proceedings of the Royal Society B 142:229–41. [aJJW]Google Scholar
van Kampen, N. G. (1976) Fluctuations in closed and open non-linear systems. In: Statistical physics, ed. Pál, L.& Szépfalusy, P.. North-Holland. [LI]Google Scholar
van Rotterdam, A., Lopes da Silva, F. H., van Den Ende, J., Veirgever, M. A. & Hermans, A. J. (1982) A model of the spatiotemporal characteristics of the alpha rhythm. Bulletin of Mathematical Biology 44:283–305. [rJJW, PLN, MJZ]CrossRefGoogle Scholar
Ventriglia, F. (1988) Computational simulation of cortical-like neural systems. Bulletin of Mathematical Biology 52:397–429. [PÉ]CrossRefGoogle Scholar
Ventriglia, F. (1990) Towards a kinetic theory of some global brain activities. Acta Neurologica 52:1–17. [PÉ]Google Scholar
Verleger, R. (1988) Event-related potentials and cognition: A critique of the context updating hypothesis and an alternative interpretation of the P3. Behavioral and Brain Sciences 11:343–427. [MM]CrossRefGoogle Scholar
Vinogradova, O. S., Brazhnik, E. S., Stafekhina, V. S. & Kitchigina, V. F. (1993) Acetylcholine, theta-rhythm and activity of hippocampus: 2. Septal input. Neuroscience 53:971–79. [EK]CrossRefGoogle Scholar
Vorobjov, N. A., Pavlik, V. D., Bakharev, B. V. & Zhadin, M. N. (1988) Spectra of electrical activity of the neocortex and hippocampus at stimulation of the reticular formation. Journal of Higher Nervous Activity 38:313–22 (in Russian). [MNZ]Google Scholar
Whittington, M. A., Traub, R. D. & Jeffreys, J. G. R. (1995) Synchronized oscillations in interneuronal networks driven by metabotropic glutamate receptor activation. Nature 373:612–15. [HRE]CrossRefGoogle ScholarPubMed
Wilczek, F. (1994) A call for a new physics. Science 266:1737–38. [LI]CrossRefGoogle Scholar
Wilson, M. A. & Bower, J. M. (1992) Cortical oscillations and temporal interactions in a computer simulation of periform cortex. Journal of Neurophysiology 67:981–95. [HL]CrossRefGoogle Scholar
Wilson, M. A. & Cowan, J. D. (1973) A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13:55–80. [aJJW, PLN]CrossRefGoogle ScholarPubMed
Wright, J. J. (1990) Reticular activation and the dynamics of neuronal networks. Biological Cybernetics 62:289–98. [aJJW]CrossRefGoogle ScholarPubMed
Wright, J. J., Kydd, R. R & Sergejew, A. A. (1990a) Autoregression models of EEG. Biological Cybernetics 62:201–10. [arJJW]CrossRefGoogle ScholarPubMed
Wright, J. J. & Liley, D. T. J. (1994) A millimetric-scale simulation of electrocortical wave dynamics based on anatomical estimates of cortical synaptic density. Network: Computation in Neural Systems 5:191–202. [aJJW]CrossRefGoogle Scholar
Wright, J. J. & Liley, D. T. J. (1995) Simulation of electrocortical waves. Biological Cybernetics 72:347–56. [arJJW]CrossRefGoogle ScholarPubMed
Wright, J. J. & Sergejew, A. A. (1991) Radial coherence, wave velocity and damping of electrocortical waves. Electroencejrfialography and Clinical Neurophysiology 79:403–12. [arJJW]CrossRefGoogle ScholarPubMed
Wright, J. J., Sergejew, A. A. & Liley, D. T. J. (1994) Computer simulation of electrocortical activity at millimetric scale. Electroencephalography and clinical Neurophysiology 90:365–75. [aJJW]CrossRefGoogle ScholarPubMed
Wright, J. J., Sergejew, A. A. & Stampfer, H. G. (1990b) Inverse filter computation of the neural impulse giving rise to the auditory evoked potential. Brain Topography 2:293–302. [aJJW]CrossRefGoogle Scholar
Wu, X. & Liljenström, H. (1994) Regulating the nonlinear dynamics of olfactory cortex. Network: Computation in Neural Systems 5:47–60. [HL]CrossRefGoogle Scholar
Yao, Y. & Freeman, W. J. (1990) Model of biological pattern recognition with spatially chaotic dynamics. Neural Networks 3(2):153–70. [HRE]CrossRefGoogle Scholar
Yeterian, E. H. & Pandya, D. N. (1988) Architectonic features of the primate brain: Implications for information processing and behavior. In: Information processing by the brain, ed. Markovich, H. J.. Hans Huber. [EK]Google Scholar
Zhadin, M. N. (1977) Model of conditioning and analysis of functional significance of electrophysiological correlates of learning. Journal of Higher Nervous Activity 27:949–56 (in Russian). [MNZ]Google Scholar
Zhadin, M. N. (1982) Theory of rhythmic processes in the cerebral cortex. Academic Press (in Russian). [MNZ]Google Scholar
Zhadin, M. N. (1984) Rhythmic processes in cerebral cortex. Journal of Theoretical Biology 108:565–95. [PLN, MNZ]CrossRefGoogle ScholarPubMed
Zhadin, M. N. (1991) Biophysical mechanisms of the EEG formation. In: Mathematical approaches to brain functioning diagnostics, ed. Dvorak, I.& Holden, A. V.. Manchester University Press. [MNZ]Google Scholar
Zhadin, M. N. (1994) Formation of rhythmic processes in the bioelectric activity of the cerebral cortex. Biophysics 39:133–50. [MNZ]Google ScholarPubMed
Zhang, G. & Simon, H. A. (1985) STM capacity for Chinese words and idioms: Chunking and acoustical loop hypotheses. Memory & Cognition 13:193–201. [LI]CrossRefGoogle ScholarPubMed