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How brains make chaos in order to make sense of the world

Published online by Cambridge University Press:  04 February 2010

Christine A. Skarda  and
Walter J. Freeman
Christine A. Skarda
Affiliation:
CREA, Ecole Polytechnique, 75005 Paris, France,
Walter J. Freeman
Affiliation:
Departement of Physiology-Anatomy, University of California, Berkeley, Calif.94720
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Abstract

Recent “connectionist” models provide a new explanatory alternative to the digital computer as a model for brain function. Evidence from our EEG research on the olfactory bulb suggests that the brain may indeed use computational mechanisms like those found in connectionist models. In the present paper we discuss our data and develop a model to describe the neural dynamics responsible for odor recognition and discrimination. The results indicate the existence of sensory- and motor-specific information in the spatial dimension of EEG activity and call for new physiological metaphors and techniques of analysis. Special emphasis is placed in our model on chaotic neural activity. We hypothesize that chaotic behavior serves as the essential ground state for the neural perceptual apparatus, and we propose a mechanism for acquiring new forms of patterned activity corresponding to new learned odors. Finally, some of the implications of our neural model for behavioral theories are briefly discussed. Our research, in concert with the connectionist work, encourages a reevaluation of explanatory models that are based only on the digital computer metaphor.

Keywords

brain theorychaosconnectionismEEGnonlinear dynamicsolfactionperceptionsensation
Type
Target Article
Information
Behavioral and Brain Sciences , Volume 10 , Issue 2 , June 1987 , pp. 161 - 173
Copyright
Copyright © Cambridge University Press 1987

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References

Abraham, R. H. & Shaw, C. D. (1985) Dynamics, the geometry of behavior, vol. 2. Ariel Press. [aCAS]Google Scholar
Ackley, D. H., Hinton, G. E., & Sejnowski, T. J. (1985). A learning algorithm for Boltzmann machines. Cognitive Science 9:147–69. [RR]Google Scholar
Anderson, J. A., Silverstein, J. W., Ritz, S. A. & Jones, R. S. (1977) Distinctive features, categorical perception, and probability learning: Some applications of a neural model. Psychological Review 84:413–51. [aCAS]CrossRefGoogle Scholar
Arbib, M. A. (1972) The metaphorical brain. Wiley-lnterscience. [DHP]Google Scholar
Ashby, W. R. (1952) Design for a brain. Chapman & Hall. [aCAS, DHP]Google Scholar
Auslander, D., Guckenheimer, J. & Oster, G. (1978) Random evolutionarily stable strategies. Theoretical Population Biology 13:276–93. [AC]CrossRefGoogle ScholarPubMed
Babloyantz, A. & Destexhe, A. (1986) Low-dimensional chaos in an instance of epilepsy. Proceedings of the National Academy of Sciences of the United States of America 83:3513–17. [a CAS, AB]CrossRefGoogle Scholar
Babloyantz, A. & Destexhe, A. (in press) Strange attractors in the human cortex. In: Temporal disorder and human oscillatory systems, ed. Rensing, L, Heiden, U. an der & Maekey, M. C.. Springer. [AB]Google Scholar
Babloyantz, A. & Kaczmarek, L. K. (1981) Self-organization in biological systems with multiple cellular contacts. Bulletin of Mathematical Biology 41:193–201. [rCAS]CrossRefGoogle Scholar
Babloyantz, A., Nicolis, C. & Salazar, M. (1985) Evidence of chaotic dynamics of brain activity during the sleep cycle. Physics Letters 111A:152. [AB]CrossRefGoogle Scholar
Baird, B. (in press) Nonlinear dynamics of pattern formation and pattern recognition in the rabbit olfactory bulb. Physica D. [aCAS]Google Scholar
Barlow, H. B. (1972) Single units and sensation: A neuron doctrine for perceptual psychology? Perception 1:371–94. [aCAS]CrossRefGoogle ScholarPubMed
Bénard, H. (1900) Les tourbillons cellulaires dans une nappe liquide. Revue Générate des Sciences Pures et Appliquées 12:1309–28. [RT]Google Scholar
Bressler, S. (1987a) Relation of olfactory bulb and cortex I: Spatial variation of bulbo-cortical interdependence. Brain Research. 409:285–93. [aCAS]CrossRefGoogle Scholar
Bressler, S. (1987b) Relation of olfactory bulb and cortex II: Model for driving of cortex by bulb. Brain Research. 409:294–301. [aCAS]CrossRefGoogle ScholarPubMed
Brown, T. H., Perkel, D. H. & Feldman, M. W. (1976) Evoked neurotransmitter release: Statistical effects of nonuniformity and nonstationarity. Proceedings of the National Academy of Sciences of the United States of America 73:2913–17. [DHP]CrossRefGoogle ScholarPubMed
Bullock, T. H. & Horridge, G. A. (1965) Structure and function in the nervous systems of invertebrates, vol. 1. W. H. Freeman. [aCAS]Google Scholar
Burns, B. D. (1958) The mammalian cerebral cortex. Edward Arnold. [aCAS]Google Scholar
Cain, W. S. (1980) Chemosensation and cognition. In: Olfaction and taste VII, ed. Van Der Starre, H.. IRL Press. [aCAS]Google Scholar
Carpenter, G. A. & Grossberg, S. (1987) A massively parallel architecture for a self-organizing neural pattern recognition machine. Computer Vision, Graphics, and Image Processing 37:54–115. [SG]CrossRefGoogle Scholar
Chatrian, G. E., Bickford, R. G. & Uihlein, A. (1960) Depth electrographic study of a fast rhythm evoked from human calcarine region by steady illumination. Electroencephalography and Clinical Neurophysiology 12:167–76. [rCAS]CrossRefGoogle ScholarPubMed
Chay, T. R. & Rinzel, J. (1985) Bursting, beating, and chaos in an excitable membrane model. Biophysical Journal 47:357–66. [DHP]CrossRefGoogle Scholar
Churchland, P. S. (1980) A perspective on mind-brain research. Journal of Philosophy 77:185–207. [RB]CrossRefGoogle Scholar
Churchland, P. S. (1986) Neurophilosophy: Toward a unified understanding of the mindbrain. MIT/Bradford. [aCAS]Google Scholar
Cohen, M. A. & Grossberg, S. (1983) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man, and Cybernetics 13:815–26. [DSL]CrossRefGoogle Scholar
Cohen, M. A. & Grossberg, S. (1986) Neural dynamics of speech and language coding: Developmental programs, perceptual grouping, and competition for short term memory. Human Neurobiology 5:1–22. [SG]Google ScholarPubMed
Conrad, M. (1986) What is the use of chaos? In: Chaos, ed. Holden, A. V.. Manchester University Press. [aCAS]Google Scholar
Cowan, J. D. (1968) Statistical mechanics of nerve nets. In: Neural networks, ed. Caianiello, E. R.. Springer-Verlag. [DHP]Google Scholar
Craik, K. (1952) The nature of explanation. Cambridge University Press. [rCAS]Google Scholar
del Castillo, J. & Katz, B. (1954) Quantal components of the end-plate potential. Journal of Physiology (London) 124:560–73. [DHP]Google Scholar
Demott, D. W. (1970) Toposcopic studies of learning. Charles C. Thomas. [rCAS, RMB]Google Scholar
Dretske, F. (1986) Boston studies in the philosophy of science. Vol. 90: Minds, machines and meaning, philosophy and technology II, ed. Mitcham, C. & Hunning, H.. Reidel. [GW]Google Scholar
Dreyfus, H. L. (1972) What computers can't do. Harper & Row. [RB]Google Scholar
Dreyfus, H. & Dreyfus, S. (1986) Mind over machine. Free Press. [aCAS]Google Scholar
Ellias, S. A. & Grossberg, S. (1975) Pattern formation, contrast control, and oscillations in the short term memory of shunting on-center off-surround networks. Biological Cybernetics 20:69–98. [SG]CrossRefGoogle Scholar
Emery, J. D. & Freeman, W. J. (1969) Pattern analysis of cortical evoked potential parameters during attention changes. Physiology and Behavior 4:60–77. [rCAS]CrossRefGoogle Scholar
Ermentrout, B., Campbell, J. & Oster, G. (1986) A model for shell patterns based on neural activity. Veliger 28(4):369–88. [aCAS]Google Scholar
Farmer, D., Hart, J. & Weidman, P. (1982) A phase space analysis of baroclinic flow. Physics Letters 91A:22–24. [AG]CrossRefGoogle Scholar
Feldman, J. A. & Ballard, D. H. (1982) Connectionist models and their properties. Cognitive Science 6:205–54. [aCAS]CrossRefGoogle Scholar
Feyerabend, P. (1978) Against method. Verso. [GW]Google Scholar
Fienberg, S. E. (1974) Stochastic models for single neurone firing trains: A survey. Biometrics 30:399–427. [DHP]CrossRefGoogle ScholarPubMed
Fodor, J. A. (1983) The modularity of mind: An essay on faculty psychology. Bradford/MIT Press. [rCAS]CrossRefGoogle Scholar
Freeman, W. J. (1972) Waves, pulses and the theory of neural masses. Progress in Theoretical Biology 2:87–165. [arCAS]CrossRefGoogle Scholar
Freeman, W. J. (1975) Mass action in the nervous system. Academic Press. [arCAS]Google Scholar
Freeman, W. J. (1978) Spatial properties of an EEG event in the olfactory bulb and cortex. Electroencephalography and Clinical Neurophysiology-EEG Journal 44:586–605. [aCAS]CrossRefGoogle ScholarPubMed
Freeman, W. J. (1979a) Nonlinear gain mediating cortical stimulus-response relations. Biological Cybernetics 33:237–47. [aCAS]CrossRefGoogle ScholarPubMed
Freeman, W. J. (1979b) Nonlinear dynamics of pleocortex manifested in the olfactory EEG. Biological Cybernetics 35:21–34. [arCAS]CrossRefGoogle ScholarPubMed
Freeman, W. J. (1979c) EEG analysis gives model of neuronal template-matching mechanism for sensory search with olfactory bulb. Biological Cybernetics 35:221–34. [aCAS]CrossRefGoogle ScholarPubMed
Freeman, W. J. (1980) Use of spatial deconvolution to compensate for distortion of EEG by volume conduction. IEEE Transactions on Biomedical Engineering 27:421–29. [aCAS]CrossRefGoogle ScholarPubMed
Freeman, W. J. (1981) A physiological hypothesis of perception. Perspectives in Biology and Medicine 24:561–92. [arCAS]CrossRefGoogle ScholarPubMed
Freeman, W. J. (1983a) Physiological basis of mental images. Biological Psychiatry 18:1107–25. [arCAS]Google ScholarPubMed
Freeman, W. J. (1983b) Dynamics of image formation by nerve cell assemblies. In: Synergetics of the brain, ed. Basar, E.. Flohr, H. & Mandell, A.. Springer-Verlag. [aCAS]Google Scholar
Freeman, W. J. (1986) Petit mal seizure spikes in olfactory bulb and cortex caused by runaway inhibition after exhaustion of excitation. Brain Research Reviews 11:259–84. [aCAS]CrossRefGoogle Scholar
Freeman, W. J. (1987a) Simulation of chaotic EEG patterns with a dynamic model of the olfactory system. Biological Cybernetics 56:139–50. [aCAS]CrossRefGoogle ScholarPubMed
Freeman, W. J. (1987b) Techniques used in the search for the physiological basis of the EEG. In: Handbook of electroencephalography and clinical neurophysiology, vol. 3A, part 2, ch. 18, ed. Gevins, A. & Remond, A.. Elsevier. [arCAS]Google Scholar
Freeman, W. J. & Ahn, S. M. (1976) Spatial and temporal characteristic frequencies of interactive neural masses. Proceedings, Institute of Electronics and Electrical Engineering, International Conference on Proc. IEEE. Intern. Conf. Cybernetics and Society 1–3:279–84 [aCAS]Google Scholar
Freeman, W. J. & Baird, B. (in press) Correlation of olfactory EEG with behavior: Spatial analysis. Behavioral Neuroscience. [aCAS]Google Scholar
Freeman, W. J. & Grajski, K. A. (in press) Correlation of olfactory EEG with behavior: Factor analysis. Behavioral Neuroscience. [aCAS]Google Scholar
Freeman, W. J. & Schneider, W. S. (1982) Changes in spatial patterns of rabbit olfactory EEG with conditioning to odors. Psychophysiology 19:44–56. [arCAS]CrossRefGoogle ScholarPubMed
Freeman, W. J. & Skarda, C. A. (1985) Spatial EEG patterns, nonlinear dynamics and perception: The neo-Sherringtonian view. Brain Research Reviews 10:147–75. [arCAS]CrossRefGoogle Scholar
Freeman, W. J. & Van Dijk, B. (submitted) Spatial patterns of visual cortical fast EEG during conditioned reflex in a rhesus monkey. [aCAS]Google Scholar
Freeman, W. J. & Viana Di Frisco, G. (1986a) EEG spatial pattern differences with discriminated odors manifest chaotic and limit cycle attractors in olfactory bulb of rabbits. In: Brain theory, ed. Palm, G.. Springer-Verlag. [aCAS]Google Scholar
Freeman, W. J. & Viana Di Frisco, G. (1986b) Correlation of olfactory EEG with behavior: Time series analysis. Behavioral Neuroscience 100:753–63. [arCAS]CrossRefGoogle Scholar
Froehling, H., Crutchfield, J., Farmer, D., Packard, N. & Shaw, R. (1981) On determining the dimension of chaotic flows. Physica 3D:605–17. [AG]Google Scholar
Garfinkel, A. (1983) A mathematics for physiology. American Journal of Physiology 245: (Regulatory, Integrative and Comparative Physiology) 14:R455–66. [arCAS]Google ScholarPubMed
Gauld, A. & Shotter, J. (1977) Human action and its psychological investigation. Routledge & Kegan Paul. [RB]Google Scholar
Gerstein, G. L. & Mandelbrot, B. (1964) Random walk models for the spike activity of a single neuron. Biophysical Journal 4:41–68. [DHP]CrossRefGoogle ScholarPubMed
Gibson, J. J. (1979) The ecological approach to visual perception. Houghton Mifflin. [aCAS]Google Scholar
Class, L. & Mackey, M. (1979) Pathological conditions resulting from instabilities in physiological control systems. Annals of New York Academy of Sciences 316:214–35. [AG]Google Scholar
Gonzalez-Estrada, M. T. & Freeman, W. J. (1980) Effects of carnosine on olfactory bulb EEG, evoked potential and DC potentials. Brain Research 202:373–86. [rCAS]CrossRefGoogle ScholarPubMed
Goodman, N. (1968) Languages of art: An approach to a theory of symbols. Bobbs-Merrill. [JAB]Google Scholar
Grajski, K., Breiman, L., Viana Di Frisco, G. & Freeman, W. J. (in press) Classification of EEG spatial patterns with a tree-structured methodology: CART [Classification and regressive trees). IEEE Transactions in Biomedical Engineering. [aCAS]Google Scholar
Grassberger, P. (1986) Do climatic attractors exist? Nature 323:609–12. [AG]CrossRefGoogle Scholar
Grassberger, P. & Procaccia, I. (1983) Measuring the strangeness of strange attractors. Physica 9D:189–208. [aCAS]Google Scholar
Gray, C. M. (1986) Centrifugal regulation of olfactory coding and response plasticity in the olfactory bulb of the conscious rabbit. Ph.D. thesis, Baylor University. [aCAS]Google Scholar
Gray, C. M., Freeman, W. J. & Skinner, J. E. (1986) Chemical dependencies of learning in the rabbit olfactory bulb: Acquisition of the transient spatial-pattern change depends on norepinephrine. Behavioral Neuroscience 100:585–96. [arCAS]CrossRefGoogle ScholarPubMed
Grossberg, S. (1975) A neural model of attention, reinforcement, and discrimination learning. International Review of Neurobiology 18:263–327. [DSL]CrossRefGoogle ScholarPubMed
Grossberg, S. (1976) Adaptive pattern classification and universal receding. 11: Feedback, expectation, olfaction, and illusions. Biological Cybernetics 23:187–202. [rCAS]CrossRefGoogle Scholar
Grossberg, S. (1980) How does the brain build a cognitive code? Psychological Review 87:1–51. [aCAS, DSL]CrossRefGoogle ScholarPubMed
Grossberg, S. (1981) Adaptive resonance in development, perception, and cognition. In: Mathematical psychology and psychophysiology, ed. Grossberg, S.. American Mathematical Society. [rCAS, SG]Google Scholar
Grossberg, S. (1982a) Studies of mind and brain: Neural principles of learning, perception, development, cognition, and motor control. Reidel. [SG]CrossRefGoogle Scholar
Grossberg, S. (1982b) Processing of expected and unexpected events during conditioning and attention: A psychophysiological theory. Psychological Review 89:529–72. [DSL]CrossRefGoogle ScholarPubMed
Grossberg, S. (1983) Neural substrates of binocular form perception: Filtering, matching, diffusion, and resonance. In: Synergetics of the brain, ed. Basar, E., Flohr, H., Haken, H. & Mandell, A. J.. Springer-Verlag. [SG]Google Scholar
Grossberg, S. (1987a) The adaptive brain. I: Cognition, learning, reinforcement, and rhythm. Elsevier/North-Holland. [SG]Google Scholar
Grossberg, S. (1987b) The adaptive brain, II: Vision, speech, language, and motor control. Elsevier/North-Holland. [SG]Google Scholar
Grossberg, S. & Levine, D. S. (submitted) Neural dynamics of attentionally modulated Pavlovian conditioning: Blocking, interstimulus interval, and secondary reinforcement. [DSL]Google Scholar
Grossberg, S. & Stone, G. O. (1986) Neural dynamics of word recognition and recall: Attentional priming, learning, and resonance. Psychological Review 93:46–74. [SG]CrossRefGoogle ScholarPubMed
Guckenheimer, J. & Holmes, P. (1983). Dynamical systems and bifurcations of vector fields. Springer. [RT]CrossRefGoogle Scholar
Hebb, D. D. (1949) The organization of behavior. Wiley. [arCAS]Google Scholar
Hinton, G. (1985) Learning in parallel networks. Byte 10:265. [aCAS]Google Scholar
Hinton, G. & Anderson, J. A. (1981) Parallel models of associative memory. Erlbaum. [aCAS]Google Scholar
Holden, A. V. ed. (1986) Chaos. Manchester University Press. [rCAS]CrossRefGoogle Scholar
Hopfield, J. J. (1982) Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences of the United States of America [arCAS, RR]Google Scholar
Hopfield, J. J. & Tank, D. W. (1986) Computing with neural circuits: A model. Science 233:625–33. [aCAS, DSL, DHP]CrossRefGoogle ScholarPubMed
Julesz, B. (1984) A brief outline in the texton theory of human vision. Trends in Neuroscience 7:41–45. [arCAS]CrossRefGoogle Scholar
Kaczmarek, L. K. & Babloyantz, A. (1977) Spatiotemporal patterns in epileptic seizures. Biological Cybernetics 26:199. [AB]CrossRefGoogle ScholarPubMed
Kohonen, T. (1984) Self-organization and associative memory. Springer-Verlag. [aCAS, JAB]Google Scholar
Lancet, D., Greer, C. A., Kauer, J. S. & Shepherd, G. M. (1982) Mapping of odor-related neuronal activity in the olfactory bulb by high-resolution 2-deoxyglueose autoradiography. Proceedings of the National Academy of Sciences of the United States of America 79:670–74. [aCAS]CrossRefGoogle ScholarPubMed
Lashley, K. S. (1942) The problem of cerebral organization in vision. In: Biological Symposia Vii, ed. Cartel, J.. Cattel, J. Press. [rCAS]Google Scholar
Layne, S. P., Mayer-Kress, G. & Holzfuss, J. (1986) Problems associated with dimensional analysis of EEG data. In: Dimensions and entropies in chaotic systems, ed. Mayer-Kress, G.. Springer. [AB]Google Scholar
Levine, D. S. (1986) A neural network model of temporal order effects in classical conditioning. In: Modelling of biomedical systems, ed. Eisenfeld, J. & Witten, M.. Elsevier. [DSL]Google Scholar
Lilly, J. C. & Cherry, R. B. (1951) Traveling waves of action and of recovery during responses and spontaneous activity in the cerebral cortex. American Journal of Physiology 167:806. [RMB]Google Scholar
Lilly, J. C. & Cherry, R. B. (1954) Surface movements of click responses from acoustical cerebral cortex of cat: Leading and trailing edges of a response figure. Journal of Neurophysiology 17:521–32. [RMB]CrossRefGoogle ScholarPubMed
Lilly, J. C. & Cherry, R. B. (1955) Surface movements of figures in spontaneous activity of anesthetized cortex: Leading and trailing edges. Journal of Neurophysiology 18:18–32. [rCAS]CrossRefGoogle ScholarPubMed
Livanov, M. N. (1977) Spatial organization of cerebral processes. Wiley. [rCAS]Google Scholar
Lorente De Nó, R. (1934) Studies in the structure of the cerebral cortex. I: The area entorhinalis. Journal von Psychologic und Neurologie 45:381–438. [rCAS]Google Scholar
Lorenz, E. (1963) Deterministic nonperiodic flow. Journal of Atmospheric Sciences 20:130–41. [AG]2.0.CO;2>CrossRefGoogle Scholar
Mandell, A. J. (1986) Complexity versus disorder in the cardiac monitoring problem: A four-minute warning. Technical report, Mathematics Institute, University of Warwick. Coventry, England. [DHP]Google Scholar
Marr, D. (1982) Vision. Freeman. [DCE]Google Scholar
Marr, D. & Poggio, T. (1976) Cooperative computation of stereo disparity. Science 194:283–87. [DCE]CrossRefGoogle ScholarPubMed
Martinez, D. M. & Freeman, W. J. (1984) Periglomerular cell action on mitral cell in olfactory bulb shown by current source density analysis. Brain Research 308:223–33. [aCAS]CrossRefGoogle ScholarPubMed
Maturana, H. R. & Varela, F. J. (1980) Boston studies in the philosophy of science. Vol. 42: Autopoiesis and cognition, ed. Cohen, R. S. & Wartofsky, M. W.. Reidel. [GW]CrossRefGoogle Scholar
May, R. M. (1976) Simple mathematical models with very complicated dynamics. Nature 261:459–67. [DHP]CrossRefGoogle ScholarPubMed
McClelland, J. L. & Rumelhart, D. E. (1981) An interactive activation model of context effects in letter perception: Part 1. Psychological Review 88:375–407. [JAB]CrossRefGoogle Scholar
McCulloch, W. S. & Pitts, W. H. (1943) A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics 5:115–33. [DHP]CrossRefGoogle Scholar
Misgeld, U., Deisz, R., Dodt, H. & Lux, H. (1986) The role of chloride transport in postsynaptic inhibition of hippocampal neurons. Science 232:1413–15. [aCAS]CrossRefGoogle ScholarPubMed
Moore, G. P., Perkel, D. H. & Segundo, J. P. (1966) Statistical analysis and functional interpretation of neuronal spike data. Annual Review of Physiology 28:493–522. [DHP]CrossRefGoogle Scholar
Moulton, D. G. (1976) Spatial patterning of response to odors in the peripheral olfactory system. Physiological Reviews 56:578–93. [aCAS]CrossRefGoogle ScholarPubMed
Mpitsos, G. J. & Cohan, C. S. (1986) Convergence in a distributed nervous system: Parallel processing and self-organization. Journal of Neurobiology 17:517–45. [DHP]CrossRefGoogle Scholar
Newberry, N. & Nicoll, R. (1985) Comparison of the action of baclofen with y-aminobutyric acid on rat hippocampal pyramidal cells in vitro. Journal of Physiology 360:161–85. [aCAS]CrossRefGoogle Scholar
Nicolis, J. S. (1985a) Hierarchical systems. Springer. [AB]Google Scholar
Nicolis, J. S. (1985b) Chaotic dynamics of information processing with relevance to cognitive brain functions. Kybernetes 14:167–73. [rCAS]CrossRefGoogle Scholar
Nicolis, J. S. & Tsuda, I. (1985) Chaotic dynamics of information processing: The “magic number seven plus-minus two” revisited. Bulletin of Mathematical Biology 47:343–65. [rCAS]Google ScholarPubMed
Oono, Y. & Kohmoto, M. (1985) Discrete model of chemical turbulence. Physical Review Letters 55:2927–31. See especially the references to the work of Kuramoto, , Yamada, et al. , most of which has been published in the journal Progress in Theoretical Physics over the past decade. [MAC]CrossRefGoogle ScholarPubMed
Pellionisz, A. & Llinás, R. (1979) Brain modeling by tensor network theory and computer simulation. The cerebellum: Distributed processor for predictive coordination. Neuroscience 4:323–48. [DHP]CrossRefGoogle ScholarPubMed
Perkel, D. H. & Bullock, T. H. (1968) Neural coding. Neurosciences Research Program Bulletin 6:221–348. [aCAS]Google Scholar
Perkel, D. H., Gerstein, G. L. & Moore, G. P. (1967a) Neuronal spike trains and stochastic point processes. I. The single spike train. Biophysical Journal 7:391–418. [DHP]CrossRefGoogle ScholarPubMed
Perkel, D. H., Gerstein, G. L. & Moore, G. P. (1967b) Neuronal spike trains and stochastic point processes. II.Google Scholar
Simultaneous spike trains. Biophysical Journal 7:419–40. [DHP]CrossRefGoogle Scholar
Pylyshyn, Z. W. (1984) Computation and cognition: Toward a foundation for cognitive science. Bradford Books/MIT Press. [aCAS]Google Scholar
Rapp, P. E., Zimmerman, I. D., Albano, A. M., Deguzman, G. C. & Greenbaun, N. N. (1985) Dynamics of spontaneous neural activity in the simian motor cortex. Physics Letters 110A:335. [AB]CrossRefGoogle Scholar
Rayleigh, Lord (John William Strutt) (1916) Philosophical Magazine 32:529–46. [RT]Google Scholar
Riemann, B. (1902) Cesammelte Werke, Nachträge. Teubner. [RT]Google Scholar
Roschke, J. & Basar, E. (in press) EEG is not a simple noise. Strange attractors in intercranial structures. In: Dynamics of sensory and cognitive signal processing in the brain, ed. Basar, E.. Springer. [AB]Google Scholar
Rosenblatt, F. (1962) Principles of neurodynamics, perceptrons and the theory of brain mechanisms. Spartan. [aCAS, DHP]Google Scholar
Rössler, O. E. (1983) The chaotic hierarchy. Zeitschrift fur Naturforschung. 38A:788–802. [arCAS]CrossRefGoogle Scholar
Ruelle, D. & Takens, F. (1971) On the nature of turbulence. Communications in Mathematical Physics 20:167 [RT]CrossRefGoogle Scholar
Rumelhart, D. E., Hinton, G. E. & Williams, R. J. (1986) Learning representations by back-propagating errors. Nature 323:533–36. [DHP]CrossRefGoogle Scholar
Rumelhart, D., McClelland, J. L. & PDP Research Group (1986) Parallel distributed processing: Explorations in the microstructures of cognition, vol. I: Foundations. MIT/Bradford. (arCAS]Google Scholar
Sampath, G. & Srinivasan, S. K. (1977) Stochastic models for spike trains of single neurons. Springer-Verlag. [DHP]CrossRefGoogle Scholar
Schuster, H. (1984) Deterministic chaos: An introduction. Physik-Verlag. [aCAS, RB]Google Scholar
Searle, J. R. (1980) Minds, brains, and programs. Behavioral and Brain Sciences 3:417–57. [RB]CrossRefGoogle Scholar
Shaw, G. L., Silverman, D. J. & Pearson, J. C. (1985) Model of cortical organization embodying a basis for a theory of information processing and memory recall. Proceedings of the National Academy of Sciences of the United States of America 82:2364–68. [DHP]CrossRefGoogle ScholarPubMed
Shaw, R. (1984) The Dripping Faucet as a Model Chaotic System. Ariel Press. [rCAS]Google Scholar
Sheer, D. (1976) Focused arousal and 40 Hz EEG. In: The neuropsychology of learning disorders: Theoretical approaches, ed. Knights, R. M. & Baker, D. J., University Park Press. [rCAS]Google Scholar
Shepherd, G. M. (1972) Synaptic organization of the mammalian olfactory bulb. Physiological Review 52:864–917. [aCAS]CrossRefGoogle ScholarPubMed
Sherrington, C. (1906) The integrative action of the nervous system. Yale University Press. [rCAS]Google Scholar
Sherrington, C. (1940) Man on his nature (rev. ed. 1953). Cambridge University Press. [DHP]Google Scholar
Skarda, C. A. (1986) Explaining behavior: Bringing the brain back in. Inquiry 29:187–202. [aCAS]CrossRefGoogle Scholar
Thom, R. (1981) Morphologie du sémiotique, recherches sémiotiques. Semiotic Inquiry 1:301–10. [RT]Google Scholar
Turner, J. S., Roux, J. C., McCormick, W. D. & Swinney, H. L. (1981) Alternating periodic and chaotic regimes in a chemical reaction — experiment and theory. Physics Letters 85A:9–14 [AC]CrossRefGoogle Scholar
Viana Di Prisco, G. (1984) Hebb synaptic plasticity. Progress in Neurobiology 22:89–102. [aCAS]CrossRefGoogle ScholarPubMed
Viana Di Prisco, G. & Freeman, W. J. (1985) Odor-related bulbar EEG spatial pattern analysis during appetitive conditioning in rabbits. Behavioral Neuroscience 99:964–78. [aCAS]CrossRefGoogle Scholar
Von Neumann, J. (1958) The computer and the brain. Yale University Press. [rCAS, DHP]Google Scholar
Waddington, C. H. (1957) The strategy of the genes. Allen and Unwin. [RT]Google Scholar
Walter, W. G. (1953) The living brain. Norton. [arCAS]Google Scholar
Whitehead, A. N. (1960) Process and reality. Harper & Row. [rCAS, RT]Google Scholar
Willey, T. J. (1973) The untrastructure of the cat olfactory bulb. Journal of Comparative Neurology 152:211–32. [aCAS]CrossRefGoogle Scholar
Wilson, D. A., Sullivan, R. M. & Leon, M. (1985) Odor familiarity alters mitral cell response in the olfactory bulb of neonatal rats. Developmental Brain Research 22:314–17. [rCAS, DHP]CrossRefGoogle Scholar
Winfree, A. T. (1980) The geometry of biological time (section 8D). Springer-Verlag. [MAC]CrossRefGoogle Scholar
Wolfram, S. (1984) Cellular automata as models of complexity. Nature 311:419–24. [DHP]CrossRefGoogle Scholar
Zucker, R. S. (1973) Changes in the statistics of transmitter release during facilitation. Journal of Physiology (London) 241:69–89. [DHP]CrossRefGoogle Scholar