Chaotic Bursts and bifurcation in Chaotic Neural Networks with Ring Structure

We investigate a noninvertible map describing burst firing in a chaotic neural network model with ring structure. Since each neuron interacts with many other neurons in biological neural systems, it is important to consider global dynamics of networks composed of nonlinear neurons in order to clarify not only mechanisms of emergence of the burst firing but also its possible functional roles. We analyze parameter regions in which burst firing can be observed, and show that dynamics of strange attractors with burst firing is related to the generation of a homoclinic-like situation and vanishing of an invariant closed curve of the map.

[1]  Eugene M. Izhikevich,et al.  Neural excitability, Spiking and bursting , 2000, Int. J. Bifurc. Chaos.

[2]  A. Selverston,et al.  Interacting biological and electronic neurons generate realistic oscillatory rhythms , 2000, Neuroreport.

[3]  Chang-song Zhou,et al.  Chaotic neural networks and chaotic annealing , 2000, Neurocomputing.

[4]  D. Plenz,et al.  A basal ganglia pacemaker formed by the subthalamic nucleus and external globus pallidus , 1999, Nature.

[5]  Junjie Wei,et al.  Qualitative analysis of a neural network model with multiple time delays , 1999 .

[6]  J. Rinzel,et al.  Oscillatory and bursting properties of neurons , 1998 .

[7]  Michael Stiber,et al.  Synaptic coding of spike trains , 1998 .

[8]  J. Bargas,et al.  Ion channels: keys to neuronal specialization , 1998 .

[9]  Thelma L. Williams,et al.  Spinal cord of Lamprey: generation of locomotor patterns , 1998 .

[10]  H. Kawakami,et al.  A Method to Calculate Homoclinic Points of a Two-Dimensional Noninvertible Map , 1997 .

[11]  S. Han,et al.  Chaotic Bursting Behavior of Coupled Neural Oscillators , 1997 .

[12]  Christian Mira,et al.  Homoclinic and Heteroclinic Situations Specific to Two-Dimensional Noninvertible Maps , 1997 .

[13]  G. Laurent,et al.  Distinct Mechanisms for Synchronization and Temporal Patterning of Odor-Encoding Neural Assemblies , 1996, Science.

[14]  Teresa Ree Chay,et al.  BURSTING, SPIKING, CHAOS, FRACTALS, AND UNIVERSALITY IN BIOLOGICAL RHYTHMS , 1995 .

[15]  G. Laurent,et al.  Encoding of Olfactory Information with Oscillating Neural Assemblies , 1994, Science.

[16]  K. H. Britten,et al.  Power spectrum analysis of bursting cells in area MT in the behaving monkey , 1994, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[17]  Christian Mira,et al.  ON BEHAVIORS OF TWO-DIMENSIONAL ENDOMORPHISMS: ROLE OF THE CRITICAL CURVES , 1993 .

[18]  Hatsuo Hayashi,et al.  Chaotic nature of bursting discharges in the Onchidium pacemaker neuron , 1992 .

[19]  James A. Yorke,et al.  CALCULATING STABLE AND UNSTABLE MANIFOLDS , 1991 .

[20]  K. Aihara,et al.  GRID IMAGING FOR A TWO-DIMENSIONAL MAP , 1991 .

[21]  K. Aihara,et al.  Chaotic neural networks , 1990 .

[22]  G. Ermentrout,et al.  Analysis of neural excitability and oscillations , 1989 .

[23]  K. Aihara,et al.  12. Chaotic oscillations and bifurcations in squid giant axons , 1986 .

[24]  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.

[25]  Stephen Grossberg,et al.  Dynamic Models of Neural Systems: Propagated Signals, Photoreceptor Transduction, and Circadian Rhythms , 1983 .

[26]  R. Kapral.  Analysis of flow hysteresis by a one-dimensional map , 1982 .