Dynamics of a competitive Lotka-Volterra system with three delays

被引：14
|
作者：
Liao, Maoxin [1 ,2 ]
Tang, Xianhua [2 ]
Xu, Changjin [2 ]
机构：
[1] Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China
[2] Cent South Univ, Sch Math Sci & Comp Technol, Changsha 410083, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 217卷 / 24期
关键词：
Lotka-Volterra system; Hopf bifurcation; Delay; Periodic solution; GLOBAL PERIODIC-SOLUTIONS; HOPF-BIFURCATION; ATTRACTIVITY; STABILITY;
D O I：
10.1016/j.amc.2011.04.078
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a competitive Lotka-Volterra system with three delays is investigated. By choosing the sum tau of three delays as a bifurcation parameter, we show that in the above system, Hopf bifurcation at the positive equilibrium can occur as tau crosses some critical values. And we obtain the formulae determining direction of Hopf bifurcation and stability of the bifurcating periodic solutions by using the normal form theory and center manifold theorem. Finally, numerical simulations supporting our theoretical results are also included. (C) 2011 Elsevier Inc. All rights reserved.
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页码：10024 / 10034
页数：11
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