Different types of bursting in Chay neuronal model

Based on actual neuronal firing activities, bursting in the Chay neuronal model is considered, in which VK, reversal potentials for K+, VC, reversal potentials for Ca2+, time kinetic constant λn and an additional depolarized current I are considered as dynamical parameters. According to the number of the Hopf bifurcation points on the upper branch of the bifurcation curve of fast subsystem, which is associated with the stable limit cycle corresponding to spiking states, different types of bursting and their respective dynamical behavior are surveyed by means of fast-slow dynamical bifurcation analysis.

[1]  G. de Vries,et al.  Multiple Bifurcations in a Polynomial Model of Bursting Oscillations , 1998 .

[2]  Ravi P. Agarwal,et al.  Ordinary and Partial Differential Equations , 2009 .

[3]  Wei Ren,et al.  Gwn-Induced bursting, Spiking, and Random subthreshold Impulsing oscillation before Hopf bifurcations in the Chay Model , 2004, Int. J. Bifurc. Chaos.

[4]  Lee A. Segel,et al.  A basic biophysical model for bursting neurons , 1993, Biological Cybernetics.

[5]  Mark Pernarowski,et al.  Fast Subsystem Bifurcations in a Slowly Varying Liénard System Exhibiting Bursting , 1994, SIAM J. Appl. Math..

[6]  Xiaojing Wang,et al.  Analysis of complex bursting in cortical pyramidal neuron models , 2000, Neurocomputing.

[7]  R. Bertram,et al.  Topological and phenomenological classification of bursting oscillations , 1995 .

[8]  Zhuoqin Yang,et al.  Transitions from bursting to spiking due to depolarizing current in the Chay neuronal model , 2007 .

[9]  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.

[10]  Thomas Erneux,et al.  Slow Passage Through a Hopf Bifurcation: From Oscillatory to Steady State Solutions , 1993, SIAM J. Appl. Math..

[11]  R. North,et al.  Burst firing in dopamine neurons induced by N-methyl-D-aspartate: role of electrogenic sodium pump. , 1992, Science.

[12]  T. Erneux,et al.  Understanding bursting oscillations as periodic slow passages through bifurcation and limit points , 1993 .

[13]  John Rinzel,et al.  A Formal Classification of Bursting Mechanisms in Excitable Systems , 1987 .

[14]  Q. Lu,et al.  The Integer Multiple "Fold/homoclinic" Bursting Induced by Noise in the Chay Neuronal Model , 2005 .

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

[16]  David Terman,et al.  Properties of a Bursting Model with Two Slow Inhibitory Variables , 1993, SIAM J. Appl. Math..

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

[18]  Thomas Erneux,et al.  Near-Threshold Bursting Is Delayed by a Slow Passage near a Limit Point , 1997, SIAM J. Appl. Math..

[19]  J. Rinzel,et al.  Dissection of a model for neuronal parabolic bursting , 1987, Journal of mathematical biology.

[20]  F. Ashcroft,et al.  Electrophysiology of the pancreatic beta-cell. , 1989, Progress in biophysics and molecular biology.

[21]  Baofeng Yang,et al.  Various tolerances to arsenic trioxide between human cortical neurons and leukemic cells , 2006, Science in China Series C: Life Sciences.

[22]  Teresa Ree Chay,et al.  Chaos in a three-variable model of an excitable cell , 1985 .

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

[24]  John Rinzel,et al.  Bursting oscillations in an excitable membrane model , 1985 .

[25]  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.

[26]  N. Kopell,et al.  Parabolic bursting revisited , 1996, Journal of mathematical biology.

[27]  John Rinzel,et al.  Analysis of bursting in a thalamic neuron model , 1994, Biological Cybernetics.

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