期刊
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
卷 7, 期 3, 页码 1101-1129出版社
SIAM PUBLICATIONS
DOI: 10.1137/070707579
关键词
piecewise linear models; gap junctions; Floquet theory; coupled-oscillator theory; phase-density function
The presence of gap junction coupling among neurons of the central nervous systems has been appreciated for some time now. In recent years there has been an upsurge of interest from the mathematical community in understanding the contribution of these direct electrical connections between cells to large-scale brain rhythms. Here we analyze a class of exactly soluble single neuron models, capable of producing realistic action potential shapes, that can be used as the basis for understanding dynamics at the network level. This work focuses on planar piecewise linear models that can mimic the. ring response of several different cell types. Under constant current injection the periodic response and phase response curve (PRC) are calculated in closed form. A simple formula for the stability of a periodic orbit is found using Floquet theory. From the calculated PRC and the periodic orbit a phase interaction function is constructed that allows the investigation of phase-locked network states using the theory of weakly coupled oscillators. For large networks with global gap junction connectivity we develop a theory of strong coupling instabilities of the homogeneous, synchronous, and splay states. For a piecewise linear caricature of the Morris-Lecar model, with oscillations arising from a homoclinic bifurcation, we show that large amplitude oscillations in the mean membrane potential are organized around such unstable orbits.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据