Bifurcation analysis for a ratio-dependent predator-prey system with multiple delays

被引：3
|
作者：
Lv, Dingyang [1 ]
Zhang, Wen [2 ,3 ]
Tang, Yi [1 ]
机构：
[1] Hunan First Normal Coll, Dept Math, Changsha 410205, Hunan, Peoples R China
[2] Hunan Univ Commerce, Sch Math & Stat, Changsha 410205, Hunan, Peoples R China
[3] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
来源：
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS | 2016年 / 9卷 / 06期
关键词：
Ratio-dependent; delay; Hopf bifurcation; center manifold; periodic solutions; POSITIVE PERIODIC-SOLUTIONS; COMPETITION SYSTEMS; HOPF-BIFURCATION; TIME DELAYS; STABILITY; EQUATIONS; NETWORKS; MODEL;
D O I：
10.22436/jnsa.009.06.03
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a ratio-dependent predator-prey system with multiple delays where the dynamics are logistic with the carrying capacity proportional to prey population. By choosing the sum tau of two delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results. (C) 2016 All rights reserved.
引用
收藏
页码：3479 / 3490
页数：12
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