ON HOPF BIFURCATION OF A DELAYED PREDATOR-PREY SYSTEM WITH DIFFUSION

被引：6

作者：

Liu, Jianxin ^{[1
]}

Wei, Junjie ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2013年 / 23卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Predator-prey system; delay; diffusion; Hopf bifurcation; PARTIAL-DIFFERENTIAL-EQUATIONS; NORMAL FORMS; STABILITY; MODEL;

D O I：

10.1142/S0218127413500235

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A delayed predator-prey system with diffusion and Dirichlet boundary conditions is considered. By regarding the growth rate a of prey as a main bifurcation parameter, we show that Hopf bifurcation occurs when the parameter a is varied. Then, by using the center manifold theory and normal form method, an explicit algorithm for determining the direction of the Hopf bifurcations and stability of the bifurcating periodic solutions is derived.

引用

页数：13

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