Bogdanov-Takens Bifurcation of a Delayed Ratio-Dependent Holling-Tanner Predator Prey System

被引：1
|
作者：
Liu, Xia [1 ]
Liu, Yanwei [2 ]
Wang, Jinling [1 ]
机构：
[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Peoples R China
[2] Shanghai Univ, Inst Syst Biol, Shanghai 200444, Peoples R China
来源：
ABSTRACT AND APPLIED ANALYSIS | 2013年
关键词：
FUNCTIONAL-RESPONSE; MULTIPLE BIFURCATIONS; MODEL; SINGULARITY;
D O I：
10.1155/2013/898015
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A delayed predator prey system with refuge and constant rate harvesting is discussed by applying the normal form theory of retarded functional differential equations introduced by Faria and Magalhaes. The analysis results show that under some conditions the system has a Bogdanov-Takens singularity. A versal unfolding of the system at this singularity is obtained. Our main results illustrate that the delay has an important effect on the dynamical behaviors of the system.
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页数：5
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