STABILITY AND HOPF BIFURCATION IN A SYMMETRIC LOTKA-VOLTERRA PREDATOR-PREY SYSTEM WITH DELAYS

被引：0

作者：

Xia, Jing ^{[1
]}

Yu, Zhixian ^{[2
]}

Yuan, Rong ^{[3
]}

机构：

[1] Peking Univ, Sch Math, Beijing 100871, Peoples R China

[2] Shanghai Univ Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China

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

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年

基金：

中国国家自然科学基金;

关键词：

Predator-prey system; delay; stability; Hopf bifurcation; normal form; FUNCTIONAL-DIFFERENTIAL EQUATIONS; GLOBAL PERIODIC-SOLUTIONS; NORMAL FORMS; MODEL;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article concerns a symmetrical Lotka-Volterra predator-prey system with delays. By analyzing the associated characteristic equation of the original system at the positive equilibrium and choosing the delay as the bifurcation parameter, the local stability and Hopf bifurcation of the system are investigated. Using the normal form theory, we also establish the direction and stability of the Hopf bifurcation. Numerical simulations suggest an existence of Hopf bifurcation near a critical value of time delay.

引用

页数：16

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