您当前所在位置: 首页 > 学者

郭上江

  • 20浏览

  • 0点赞

  • 0收藏

  • 0分享

  • 58下载

  • 0评论

  • 引用

期刊论文

Non-linear waves in a ring of neurons

郭上江SHANGJIANG GUO† AND LIHONG HUANG

IMA Journal of Applied Mathematics(2006)71, 496-518,-0001,():

URL:

摘要/描述

In this paper, we study the effect of synaptic delay of signal transmission on the pattern formation and some properties of non-linear waves in a ring of identical neurons. First, linear stability of the model is investigated by analyzing the associated characteristic transcendental equation. Regarding the delay as a bifurcation parameter, we obtained the spontaneous bifurcation of multiple branches of periodic solutions and their spatio-temporal patterns. Second, global continuation conditions for Hopf bifurcating periodic orbits are derived by using the equivariant degree theory developed by Geba et al. and independently by Ize & Vignoli. Third, we show that the coincidence of these periodic solutions is completely determined either by a scalar delay differential equation if the number of neurons is odd, or by a system of two coupled delay differential equations if the number of neurons is even. Fourth, we summarize some important results about the properties of Hopf bifurcating periodic orbits, including the direction of Hopf bifurcation, stability of the Hopf bifurcating periodic orbits, and so on. Fifth, in an excitatory ring network, solutions of most initial conditions tend to stable equilibria, the boundary separating the basin of attraction of these stable equilibria contains all of periodic orbits and homoclinic orbits. Finally, we discuss a trineuron network to illustrate the theoretical results obtained in this paper and conclude that these theoretical results are important to complement the experimental and numerical observations made in living neurons systems and artificial neural networks, in order to understand the mechanisms underlying the system dynamics better.

版权说明:以下全部内容由郭上江上传于   2010年01月07日 11时20分54秒,版权归本人所有。

我要评论

全部评论 0

本学者其他成果

    同领域成果