Bifurcation Phenomena in a Lotka-Volterra Model with Cross-Diffusion and Delay Effect

被引：14

作者：

Yan, Shuling ^{[1
]}

Guo, Shangjiang ^{[1
]}

机构：

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2017年 / 27卷 / 07期

关键词：

Cross-diffusion; Lyapunov-Schmidt reduction; Hopf bifurcation; steady-state solution; PREY-PREDATOR SYSTEM; HOPF-BIFURCATION; POPULATION-MODEL; STABILITY; STATES;

D O I：

10.1142/S021812741750105X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper focuses on a Lotka-Volterra model with delay and cross-diffusion. By using Lyapunov-Schmidt reduction, we investigate the existence, multiplicity, stability and Hopf bifurcation of spatially nonhomogeneous steady-state solutions. Furthermore, we obtain some criteria to determine the bifurcation direction and stability of Hopf bifurcating periodic orbits by using Lyapunov-Schmidt reduction.

引用

页数：24

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