Hopf bifurcation from spike solutions for the weak coupling Gierer-Meinhardt system

被引：8
|
作者：
Gomez, Daniel [1 ]
Mei, Linfeng [2 ]
Wei, Juncheng [1 ]
机构：
[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
[2] Zhejiang Normal Univ, Coll Math & Comp Sci, Jinhua 321004, Zhejiang, Peoples R China
来源：
EUROPEAN JOURNAL OF APPLIED MATHEMATICS | 2021年 / 32卷 / 01期
基金：
中国国家自然科学基金; 加拿大自然科学与工程研究理事会;
关键词：
Gierer-Meinhard system; Hopf bifurcation; unstable limit cycle; spike solution; nonlinear eigenvalue problem; STABILITY; DYNAMICS; PATTERNS;
D O I：
10.1017/S0956792520000066
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Hopf bifurcation from spike solutions for the classical Gierer-Meinhardt system in a one-dimensional interval is considered. The existence of time-periodic solution near the Hopf bifurcation parameter for a boundary spike is rigorously proved by the classical Crandall-Rabinowitz theory. The criteria for the stability of the limit cycle are determined, and it is shown that the limit cycle is unstable.
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页码：113 / 145
页数：33
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