Topological and phenomenological classification of bursting oscillations.

[1]  O. Masory,et al.  Numerical Integration of Ordinary Differential Equations , 2009 .

[2]  A. Sherman,et al.  Phase independent resetting in relaxation and bursting oscillators. , 1994, Journal of theoretical biology.

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

[4]  S. Gueron,et al.  Mapping the dynamics of a bursting neuron. , 1993, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[5]  D. A. Baxter,et al.  Nonlinear dynamics in a model neuron provide a novel mechanism for transient synaptic inputs to produce long-term alterations of postsynaptic activity. , 1993, Journal of neurophysiology.

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

[7]  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.

[8]  J. Byrne,et al.  Simulation of the bursting activity of neuron R15 in Aplysia: role of ionic currents, calcium balance, and modulatory transmitters. , 1991, Journal of neurophysiology.

[9]  J. Rinzel,et al.  A model of the T-type calcium current and the low-threshold spike in thalamic neurons. , 1991, Journal of neurophysiology.

[10]  R. Traub,et al.  A model of a CA3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances. , 1991, Journal of neurophysiology.

[11]  J. Rinzel,et al.  The slow passage through a Hopf bifurcation: delay, memory effects, and resonance , 1989 .

[12]  Teresa Ree Chay,et al.  Endogenous Bursting Patterns in Excitable Cells , 1988 .

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

[14]  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.

[15]  Stephen Schecter,et al.  The saddle-node separatrix-loop bifurcation , 1987 .

[16]  M. Pirchio,et al.  The ventral and dorsal lateral geniculate nucleus of the rat: intracellular recordings in vitro. , 1987, The Journal of physiology.

[17]  John Guckenheimer,et al.  Multiple bifurcation problems for chemical reactors , 1986 .

[18]  G. Ermentrout,et al.  Parabolic bursting in an excitable system coupled with a slow oscillation , 1986 .

[19]  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.

[20]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

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

[22]  John Rinzel,et al.  Bursting phenomena in a simplified Oregonator flow system model , 1982 .

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

[24]  M. Kim,et al.  Mathematical description of a bursting pacemaker neuron by a modification of the Hodgkin-Huxley equations. , 1976, Biophysical journal.

[25]  P M Dean,et al.  Glucose‐induced electrical activity in pancreatic islet cells , 1970, The Journal of physiology.

[26]  B. O. Alving Spontaneous Activity in Isolated Somata of Aplysia Pacemaker Neurons , 1968, The Journal of general physiology.

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

[28]  G. Dahlquist Convergence and stability in the numerical integration of ordinary differential equations , 1956 .

[29]  J. Sotomayor,et al.  GENERIC 3-PARAMETER FAMILIES OF PLANAR VECTOR-FIELDS, UNFOLDINGS OF SADDLE, FOCUS AND ELLIPTIC-SINGULARITIES WITH NILPOTENT LINEAR PARTS , 1991 .

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

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

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

[33]  P. Holmes,et al.  Local Codimension Two Bifurcations of Flows , 1983 .

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

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

[36]  C. A. G. Wiersma,et al.  Invertebrate nervous systems : their significance for mammalian neurophysiology , 1967 .

[37]  Peter Fgldibk,et al.  Library of Congress Cataloging-in-publication Data Sparse Coding in the Primate Cortex , 2022 .