Rapid synchronization through fast threshold modulation

Synchronization properties of locally coupled neural oscillators were investigated analytically and by computer simulation. When coupled in a manner that mimics excitatory chemical synapses, oscillators having more than one time scale (relaxation oscillators) are shown to approach synchrony using mechanisms very different from that of oscillators with a more sinusoidal waveform. The relaxation oscillators make critical use of fast modulations of their thresholds, leading to a rate of synchronization relatively independent of coupling strength within some basin of attraction; this rate is faster for oscillators that have conductance-based features than for neural caricatures such as the FitzHugh-Nagumo equations that lack such features. Computer simulations of one-dimensional arrays show that oscillators in the relaxation regime synchronize much more rapidly than oscillators with the same equations whose parameters have been modulated to yield a more sinusoidal waveform. We present a heuristic explanation of this effect based on properties of the coupling mechanisms that can affect the way the synchronization scales with array length. These results suggest that the emergent synchronization behavior of oscillating neural networks can be dramatically influenced by the intrinsic properties of the network components. Possible implications for perceptual feature binding and attention are discussed.

[1]  G. Ermentrout,et al.  Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I. , 1984 .

[2]  Ch. von der Malsburg,et al.  A neural cocktail-party processor , 1986, Biological Cybernetics.

[3]  S. Grossberg.  Contour Enhancement , Short Term Memory , and Constancies in Reverberating Neural Networks , 1973 .

[4]  H Sompolinsky,et al.  Global processing of visual stimuli in a neural network of coupled oscillators. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

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

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

[7]  R. FitzHugh.  Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[8]  F Bezanilla,et al.  Nerve membrane excitation without threshold. , 1970, Proceedings of the National Academy of Sciences of the United States of America.

[9]  C. Morris,et al.  Voltage oscillations in the barnacle giant muscle fiber. , 1981, Biophysical journal.

[10]  S. Grossberg,et al.  Some physiological and biochemical consequences of psychological postulates. , 1968, Proceedings of the National Academy of Sciences of the United States of America.

[11]  G. Ermentrout.  The behavior of rings of coupled oscillators , 1985, Journal of mathematical biology.

[12]  G. Ermentrout,et al.  Multiple pulse interactions and averaging in systems of coupled neural oscillators , 1991 .

[13]  M M Sondhi,et al.  Model for visual luminance discrimination and flicker detection. , 1968, Journal of the Optical Society of America.

[14]  R. Eckhorn,et al.  Coherent oscillations: A mechanism of feature linking in the visual cortex? , 1988, Biological Cybernetics.

[15]  S. Yoshizawa,et al.  An Active Pulse Transmission Line Simulating Nerve Axon , 1962, Proceedings of the IRE.

[16]  Rodney Cotterill,et al.  Models of brain function , 1989 .

[17]  S. Grossberg,et al.  Adaptive pattern classification and universal recoding: I. Parallel development and coding of neural feature detectors , 1976, Biological Cybernetics.

[18]  S. Grossberg.  Studies of mind and brain : neural principles of learning, perception, development, cognition, and motor control , 1982 .

[19]  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.

[20]  Stephen Grossberg,et al.  Adaptive pattern classification and universal recoding: II. Feedback, expectation, olfaction, illusions , 1976, Biological Cybernetics.

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

[22]  N. K. Rozov,et al.  Differential Equations with Small Parameters and Relaxation Oscillations , 1980 .

[23]  J. Kelso,et al.  A synergetic theory of environmentally-specified and learned patterns of movement coordination , 2004, Biological Cybernetics.

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

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

[26]  William H. Press,et al.  Numerical Recipes in FORTRAN - The Art of Scientific Computing, 2nd Edition , 1987 .

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

[28]  R. Harris-Warrick,et al.  Multiple mechanisms of bursting in a conditional bursting neuron , 1987, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[29]  G. Ermentrout,et al.  Phase transition and other phenomena in chains of coupled oscilators , 1990 .

[30]  W. Freeman.  The physiology of perception. , 1991, Scientific American.

[31]  J. Kelso,et al.  A synergetic theory of environmentally-specified and learned patterns of movement coordination , 2004, Biological Cybernetics.

[32]  G. Ermentrout,et al.  Symmetry and phaselocking in chains of weakly coupled oscillators , 1986 .

[33]  S. Strogatz,et al.  Dynamics of a globally coupled oscillator array , 1991 .

[34]  S. Strogatz,et al.  Synchronization of pulse-coupled biological oscillators , 1990 .

[35]  W. Singer,et al.  Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[36]  H. Schuster,et al.  A model for neuronal oscillations in the visual cortex , 1990, Biological Cybernetics.

[37]  J. Rinzel,et al.  Rhythmogenic effects of weak electrotonic coupling in neuronal models. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[38]  Hansel,et al.  Clustering in globally coupled phase oscillators. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[39]  A. Treisman.  Perceptual grouping and attention in visual search for features and for objects. , 1982, Journal of experimental psychology. Human perception and performance.

[40]  S. Grossberg,et al.  Pattern formation, contrast control, and oscillations in the short term memory of shunting on-center off-surround networks , 1975, Biological Cybernetics.

[41]  H. Schuster,et al.  A model for neuronal oscillations in the visual cortex , 1990, Biological Cybernetics.

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