Voltage interval mappings for activity transitions in neuron models for elliptic bursters

PHYSICA D-NONLINEAR PHENOMENA

卷:240

Article

Shilnikov, Andrey¹ 

[1] Georgia State Univ, Inst Neurosci, Atlanta, GA 30303 USA

关键词: Poincare mapping;    Elliptic;    Bursting;    Neuron model;    Bifurcation;    Periodic orbit;   

DOI  :  10.1016/j.physd.2011.04.003

来源: Elsevier

【 摘 要 】

We performed a thorough bifurcation analysis of a mathematical elliptic bursting model, using a computer-assisted reduction to equationless, one-dimensional Poincare mappings for a voltage interval. Using the interval mappings, we were able to examine in detail the bifurcations that underlie the complex activity transitions between: tonic spiking and bursting, bursting and mixed-mode oscillations, and finally mixed-mode oscillations and quiescence in the FitzHugh-Nagumo-Rinzel model. We illustrate the wealth of information, qualitative and quantitative, that was derived from the Poincare mappings, for the neuronal models and for similar (electro)chemical systems. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free