Autonomous bursting in a homoclinic system.

The output of a dynamical system in a regime of homoclinic chaos transforms from a continuous train of irregularly spaced spikes to clusters of regularly spaced spikes with quiescent periods in between (bursting), provided a low frequency portion of the output is fed back. We provide experimental evidence of such an autonomous bursting by a CO2 laser with feedback. The phenomena here presented are extremely robust against noise and display qualitative analogies with bursting phenomena in neurons.

[1]  Alexander N. Pisarchik,et al.  Theoretical and experimental study of discrete behavior of Shilnikov chaos in a CO2 laser , 2001 .

[2]  S. Levin Lectu re Notes in Biomathematics , 1983 .

[3]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[4]  Meucci,et al.  Laser dynamics with competing instabilities. , 1987, Physical review letters.

[5]  Mikhail I. Rabinovich,et al.  Self-regularization of chaos in neural systems: experimental and theoretical results , 1997 .

[6]  P. Haydon,et al.  Physiological astrocytic calcium levels stimulate glutamate release to modulate adjacent neurons. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[7]  P E Rapp,et al.  Oscillations in calcium-cyclic AMP control loops form the basis of pacemaker activity and other high frequency biological rhythms. , 1977, Journal of theoretical biology.

[8]  M. Steriade Corticothalamic resonance, states of vigilance and mentation , 2000, Neuroscience.

[9]  E. Teramoto,et al.  Mathematical Topics in Population Biology, Morphogenesis and Neurosciences , 1987 .

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

[11]  M. Steriade,et al.  Thalamic bursting mechanism: an inward slow current revealed by membrane hyperpolarization , 1982, Brain Research.

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

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

[14]  N. Rulkov Regularization of synchronized chaotic bursts. , 2000, Physical review letters.

[15]  J. Kurths,et al.  Coherence Resonance in a Noise-Driven Excitable System , 1997 .

[16]  J. Rinzel,et al.  Emergence of organized bursting in clusters of pancreatic beta-cells by channel sharing. , 1988, Biophysical journal.

[17]  R K Wong,et al.  Afterpotential generation in hippocampal pyramidal cells. , 1981, Journal of neurophysiology.

[18]  S. Lowen The Biophysical Journal , 1960, Nature.

[19]  J. L. Hudson,et al.  An experimental study of multiple peak periodic and nonperiodic oscillations in the Belousov–Zhabotinskii reaction , 1979 .

[20]  Meucci,et al.  Discrete homoclinic orbits in a laser with feedback , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  R. Keynes The ionic channels in excitable membranes. , 1975, Ciba Foundation symposium.

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

[23]  F T Arecchi,et al.  Synchronization of homoclinic chaos. , 2001, Physical review letters.

[24]  James P. Keener,et al.  Mathematical physiology , 1998 .

[25]  J. Velazquez,et al.  Bursting in inhibitory interneuronal networks: A role for gap-junctional coupling. , 1999, Journal of neurophysiology.

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

[27]  P E Rapp,et al.  A comparative survey of the function, mechanism and control of cellular oscillators. , 1979, The Journal of experimental biology.

[28]  A. Selverston,et al.  Synchronous Behavior of Two Coupled Biological Neurons , 1998, chao-dyn/9811010.

[29]  J. Hindmarsh,et al.  A model of neuronal bursting using three coupled first order differential equations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[30]  J. Keizer,et al.  Minimal model for membrane oscillations in the pancreatic beta-cell. , 1983, Biophysical journal.