Stability and Hopf Bifurcation Analysis for a Two-Species Commensalism System with Delay

被引：21

作者：

Li, Tianyang ^{[1
]}

Wang, Qiru ^{[1
]}

机构：

[1] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Guangdong, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2021年 / 20卷 / 03期

基金：

中国国家自然科学基金;

关键词：

A two-species commensalism system; Time delay; Stability; Hopf bifurcation; DIFFERENTIAL EQUATIONS; PERIODIC-SOLUTIONS; AMENSALISM MODEL;

D O I：

10.1007/s12346-021-00524-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to studying the dynamics of a two-species commensalism system with delay. By analyzing the characteristic equation and regarding the time delay as the bifurcation parameter, we investigate the local asymptotic stability of the positive equilibrium and show the existence of periodic solutions bifurcating from the positive equilibrium. Then, we derive the precise formulae to determine the Hopf bifurcation direction and the stability of the bifurcating periodic solutions by using the normal form theory and the center manifold theorem. Numerical simulation results are also included to support our theoretical analysis.

引用

页数：20

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