Bifurcation phenomena from standing pulse solutions in some reaction-diffusion systems

被引：10

作者：

Ikeda H. ^{[1
]}

Ikeda T. ^{[2
]}

机构：

[1] Department of Mathematics, Toyama University

[2] Department of Applied Mathematics and Informatics, Ryukoku University

来源：

Journal of Dynamics and Differential Equations | 2000年 / 12卷 / 1期

关键词：

Hopf bifurcation; Reaction-diffusion system; Singular perturbation; Stability; Standing pulses;

D O I：

10.1023/A:1009098719440

中图分类号：

学科分类号：

摘要：

Bifurcation phenomena from standing pulse solutions of the problem ετut = ε2uxx, + f(u, v), v t = vxx + g(u, v) is considered. ε(>0) is a sufficiently small parameter and τ is a positive one. It is shown that there exist two types of destabilization of standing pulse solutions when τ decreases. One is the appearance of travelling pulse solutions via the static bifurcation and the other is that of in-phase breathers via the Hopf bifurcation. Furthermore which type of destabilization occurs first with decreasing τ is discussed for the piecewise linear nonlinearities f and g. © 2000 Plenum Publishing Corporation.

引用

页码：117 / 167

页数：50

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