Synchronization and desynchronization in a network of locally coupled Wilson-Cowan oscillators

A network of Wilson-Cowan (WC) oscillators is constructed, and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis. The network is a 2D matrix, where each oscillator is coupled only to its neighbors. We show analytically that a chain of locally coupled oscillators (the piecewise linear approximation to the WC oscillator) synchronizes, and we present a technique to rapidly entrain finite numbers of oscillators. The coupling strengths change on a fast time scale based on a Hebbian rule. A global separator is introduced which receives input from and sends feedback to each oscillator in the matrix. The global separator is used to desynchronize different oscillator groups. Unlike many other models, the properties of this network emerge from local connections that preserve spatial relationships among components and are critical for encoding Gestalt principles of feature grouping. The ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure/ground segregation based on oscillatory correlation.

[1]  Pierre Baldi,et al.  Computing with Arrays of Coupled Oscillators: An Application to Preattentive Texture Discrimination , 1990, Neural Computation.

[2]  Peter König,et al.  Stimulus-Dependent Assembly Formation of Oscillatory Responses: I. Synchronization , 1991, Neural Computation.

[3]  W. Singer,et al.  Interhemispheric synchronization of oscillatory neuronal responses in cat visual cortex , 1991, Science.

[4]  G. Ermentrout,et al.  Oscillator death in systems of coupled neural oscillators , 1990 .

[5]  Haim Sompolinsky,et al.  Stimulus-Dependent Synchronization of Neuronal Assemblies , 1993, Neural Computation.

[6]  M. Grattarola,et al.  Necessary and sufficient conditions for synchronization of nonlinear oscillators with a given class of coupling , 1977 .

[7]  Peter König,et al.  Stimulus-Dependent Assembly Formation of Oscillatory Responses: II. Desynchronization , 1991, Neural Computation.

[8]  A. Treisman,et al.  A feature-integration theory of attention , 1980, Cognitive Psychology.

[9]  DeLiang Wang,et al.  An Oscillatory Correlation Theory of Temporal Pattern Segmentation , 1995 .

[10]  DeLiang Wang,et al.  Locally excitatory globally inhibitory oscillator networks , 1995, IEEE Transactions on Neural Networks.

[11]  Daido,et al.  Lower critical dimension for populations of oscillators with randomly distributed frequencies: A renormalization-group analysis. , 1988, Physical review letters.

[12]  DeLiang Wang,et al.  Modeling Global Synchrony in the Visual Cortex by Locally Coupled Neural Oscillators , 1994 .

[13]  S W Keele,et al.  Tests of a temporal theory of attentional binding. , 1988, Journal of experimental psychology. Human perception and performance.

[14]  Richard Bellman,et al.  Introduction to Matrix Analysis , 1972 .

[15]  J. Cowan,et al.  Temporal oscillations in neuronal nets , 1979, Journal of mathematical biology.

[16]  I. Biederman,et al.  Dynamic binding in a neural network for shape recognition. , 1992, Psychological review.

[17]  K. Bar-Eli,et al.  On the stability of coupled chemical oscillators , 1985 .

[18]  E. White.  Cortical Circuits , 1989, Birkhäuser Boston.

[19]  I. Rock,et al.  The legacy of Gestalt psychology. , 1990, Scientific American.

[20]  M. Alexander,et al.  Principles of Neural Science , 1981 .

[21]  W. Freeman.  Spatial properties of an EEG event in the olfactory bulb and cortex. , 1978, Electroencephalography and clinical neurophysiology.

[22]  E. Fetz,et al.  Coherent 25- to 35-Hz oscillations in the sensorimotor cortex of awake behaving monkeys. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[23]  Deliang Wang,et al.  Global competition and local cooperation in a network of neural oscillators , 1995 .

[24]  Steven H. Strogatz,et al.  Phase-locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies , 1988 .

[25]  Andreas G. Andreou,et al.  VLSI Phase Locking Architectures for Feature Linking in Multiple Target Tracking Systems , 1993, NIPS.

[26]  I. Biederman.  Recognition-by-components: a theory of human image understanding. , 1987, Psychological review.

[27]  Large Populations of Coupled Chemical Oscillators , 1980 .

[28]  G. Ermentrout.  Oscillator death in populations of “all to all” coupled nonlinear oscillators , 1990 .

[29]  Joachim M. Buhmann,et al.  Pattern Segmentation in Associative Memory , 1990, Neural Computation.

[30]  F. Bloom.  Principles of Neural Science, 3rd ed , 1993 .

[31]  M. Usher,et al.  Segmentation, Binding, and Illusory Conjunctions , 1991, Neural Computation.

[32]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[33]  P König,et al.  Synchronization of oscillatory neuronal responses between striate and extrastriate visual cortical areas of the cat. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[34]  Sompolinsky,et al.  Cooperative dynamics in visual processing. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[35]  Stephen Grossberg,et al.  Synchronized oscillations during cooperative feature linking in a cortical model of visual perception , 1991, Neural Networks.

[36]  G. Edelman,et al.  Reentrant signaling among simulated neuronal groups leads to coherency in their oscillatory activity. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[37]  F. Crick.  Function of the thalamic reticular complex: the searchlight hypothesis. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[38]  G. Ermentrout,et al.  Amplitude response of coupled oscillators , 1990 .

[39]  S. Zeki.  The visual image in mind and brain. , 1992, Scientific American.

[40]  J. Donoghue,et al.  Oscillations in local field potentials of the primate motor cortex during voluntary movement. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[41]  P. Milner.  A model for visual shape recognition. , 1974, Psychological review.

[42]  P. Holmes,et al.  The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model , 1982, Journal of mathematical biology.

[43]  Kim L. Boyer,et al.  Perceptual organization in computer vision: a review and a proposal for a classificatory structure , 1993, IEEE Trans. Syst. Man Cybern..

[44]  Professor Moshe Abeles,et al.  Local Cortical Circuits , 1982, Studies of Brain Function.

[45]  S. Makeig,et al.  A 40-Hz auditory potential recorded from the human scalp. , 1981, Proceedings of the National Academy of Sciences of the United States of America.

[46]  Kannan,et al.  ON IMAGE SEGMENTATION TECHNIQUES , 2022 .

[47]  L. Abbott.  A network of oscillators , 1990 .

[48]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[49]  Buhmann.  Oscillations and low firing rates in associative memory neural networks. , 1989, Physical review. A, General physics.

[50]  G. Edelman.  Neural Darwinism: The Theory Of Neuronal Group Selection , 1989 .

[51]  Richard Bellman,et al.  Introduction to matrix analysis (2nd ed.) , 1997 .

[52]  Y. Kuramoto,et al.  Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities , 1987 .

[53]  G. A. Miller.  THE PSYCHOLOGICAL REVIEW THE MAGICAL NUMBER SEVEN, PLUS OR MINUS TWO: SOME LIMITS ON OUR CAPACITY FOR PROCESSING INFORMATION 1 , 1956 .

[54]  W. Singer,et al.  Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties , 1989, Nature.

[55]  I. Schreiber,et al.  Strange attractors in coupled reaction-diffusion cells , 1982 .

[56]  DeLiang Wang,et al.  Emergent synchrony in locally coupled neural oscillators , 1995, IEEE Trans. Neural Networks.

[57]  Hansel,et al.  Synchronization and computation in a chaotic neural network. , 1992, Physical review letters.

[58]  Christoph von der Malsburg,et al.  The Correlation Theory of Brain Function , 1994 .

[59]  Leslie S. Smith,et al.  Constraints on Synchronizing Oscillator Networks , 1993, Neural Computation.

[60]  B. Baird.  Nonlinear dynamics of pattern formation and pattern recognition in the rabbit olfactory bulb , 1986 .