Hopf bifurcation analysis of a predator-prey system with Holling type IV functional response and time delay

被引：44
作者：
Lian, Fuyun [1 ,2 ]
Xu, Yuantong [1 ]
机构：
[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China
[2] Ocean Univ China, Dept Math, Qingdao 266071, Shandong, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 215卷 / 04期
关键词：
Predator-prey system; Holling IV; Time delay; Hopf bifurcation; Center manifold; GLOBAL STABILITY; MODEL;
D O I：
10.1016/j.amc.2009.07.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with a predator-prey system with Holling type IV functional response and time delay. Our aim is to investigate how the time delay affects the dynamics of the predator-prey system. By choosing the delay as a bifurcation parameter, the local asymptotic stability of the positive equilibrium and existence of local Hopf bifurcations are analyzed. Based on the normal form and the center manifold theory, the formulaes for determining the properties of Hopf bifurcation of the predator-prey system are derived. Finally, to support these theoretical results, some numerical simulations are given to illustrate the results. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：1484 / 1495
页数：12
相关论文
共 17 条
[1]   The stability and Hopf bifurcation for a predator-prey system with time delay [J].
Celik, Canan .
CHAOS SOLITONS & FRACTALS, 2008, 37 (01) :87-99
[2]   The effects of the functional response on the bifurcation behavior of a mite predator-prey interaction model [J].
Collings, JB .
JOURNAL OF MATHEMATICAL BIOLOGY, 1997, 36 (02) :149-168
[3]  
Hale J., 1993, INTRO FUNCTIONAL DIF, DOI [10.1007/978-1-4612-4342-7, DOI 10.1007/978-1-4612-4342-7]
[4]  
Hassard BD, 1981, THEORY APPL HOPF BIF
[5]  
Holling C. S., 1965, MEM ENTOMOL SOC CAN, V46, P1
[6]   GLOBAL STABILITY FOR A CLASS OF PREDATOR-PREY SYSTEMS [J].
HSU, SB ;
HUANG, TW .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1995, 55 (03) :763-783
[7]   Hopf bifurcation analysis for a predator-prey system of Holling and Leslie type [J].
Hsu, SB ;
Hwang, TW .
TAIWANESE JOURNAL OF MATHEMATICS, 1999, 3 (01) :35-53
[8]  
LESLIE PH, 1960, BIOMETRIKA, V47, P219, DOI 10.2307/2333294
[9]   Bifurcations of a predator-prey system of Holling and Leslie types [J].
Li, Yilong ;
Xiao, Dongmei .
CHAOS SOLITONS & FRACTALS, 2007, 34 (02) :606-620
[10]   Delay induced oscillation in predator-prey system with Beddington-DeAngelis functional response [J].
Lin, Guojian ;
Hong, Yiguang .
APPLIED MATHEMATICS AND COMPUTATION, 2007, 190 (02) :1296-1311
12