Bogdanov-Takens Bifurcation of a Class of Delayed Reaction-Diffusion System

被引：6

作者：

Cao, Jianzhi ^{[1
]}

Wang, Peiguang ^{[1
]}

Yuan, Rong ^{[2
]}

Mei, Yingying ^{[2
]}

机构：

[1] Hebei Univ, Coll Math & Informat Sci, Baoding 071002, Peoples R China

[2] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2015年 / 25卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Reaction-diffusion; Bogdanov-Takens singularity; delay; normal form; codimension two bifurcation; PREDATOR-PREY SYSTEM; DIFFERENTIAL-EQUATIONS; NORMAL FORMS;

D O I：

10.1142/S0218127415500820

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a class of reaction-diffusion system with Neumann boundary condition is considered. By analyzing the generalized eigenvector associated with zero eigenvalue, an equivalent condition for the determination of Bogdonov-Takens (B-T) singularity is obtained. Next, by using center manifold theorem and normal form method, we have a two-dimension ordinary differential system on its center manifold. Finally, two examples show that the given algorithm is effective.

引用

页数：11

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