报告题目：Stability, Bifurcation and Pattern Formation in a Ring Network with Delay

内容简介：After introducing some background about dynamical system, neural network and delay differential equation, we consider a ring neural network of identical elements with time delayed, nearest neighbor coupling. We give some global and local stability results and show how the presence of time delay allows for mode interactions leading to the coexistence of different oscillation patterns. The Hopf and equivariant Hopf bifurcations are analyzed. Regarding the coupling strengths as bifurcation parameters, we obtain codimension one bifurcation and the interaction of each critical bifurcations. Concrete formulae for the normal form coefficients are derived via the center manifold reduction that provide detailed information about the bifurcation and stability of various bifurcated solutions.

报 告 人：加拿大纽芬兰纪念大学 袁源 教授

袁源教授的研究领域为微分方程与动力系统的理论及应用。袁源教授是该领域内国际上最活跃的年轻学者之一，在泛函微分方程分支理论和规范性的算法方面取得了一批国际同行公认的好结果。

时   间：2009年3月4日15:30-16:30

地   点：理学院3楼会议室