文献类型：期刊文献

英文题名：Stability and Hopf Bifurcation of a Delayed Density-Dependent Predator-Prey System with Beddington-DeAngelis Functional Response

作者：Li, Haiyin[1];Meng, Gang[2];She, Zhikun[3,4]

第一作者：李海银

通讯作者：She, ZK[1];She, ZK[2]

机构：[1]Henan Univ Econ & Law, Sch Math & Informat, Jinshui East Rd, Zhengzhou 450002, Peoples R China;[2]Univ Chinese Acad Sci, Sch Math Sci, Yuquan Rd 19, Beijing 100049, Peoples R China;[3]Beihang Univ, LMIB, Xueyuan Rd 37, Beijing 100191, Peoples R China;[4]Beihang Univ, Sch Math & Syst Sci, Xueyuan Rd 37, Beijing 100191, Peoples R China

第一机构：河南财经政法大学数学与信息科学学院

通讯机构：[1]corresponding author), Beihang Univ, LMIB, Xueyuan Rd 37, Beijing 100191, Peoples R China;[2]corresponding author), Beihang Univ, Sch Math & Syst Sci, Xueyuan Rd 37, Beijing 100191, Peoples R China.

年份：2016

卷号：26

期号：10

外文期刊名：INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

收录：;EI(收录号：20163902856400);Scopus(收录号：2-s2.0-84988638353);WOS:【SCI-EXPANDED(收录号:WOS:000384073700009)】；

基金：This work was partly supported by NSFC-11422111, NSFC-11371047, NSFC-11290141 and Science and Technology Project of Henan Province-152102310320.

语种：英文

外文关键词：Stability switches; Hopf bifurcation; density dependence; Beddington-DeAngelis functional response

摘要：In this paper, we investigate the stability and Hopf bifurcation of a delayed density-dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered such that the studied predator-prey system conforms to the realistically biological environment. We start with the geometric criterion introduced by Beretta and Kuang [2002] and then investigate the stability of the positive equilibrium and the stability switches of the system with respect to the delay parameter tau. Especially, we generalize the geometric criterion in [Beretta & Kuang, 2002] by introducing the condition (i') which can be assured by the condition (H-2'), and adopting the technique of lifting to define the function (S) over tilde (n)(tau)s for alternatively determining stability switches at the zeroes of (S) over tilde (n)(tau)s. Afterwards, by the Poincare normal form for Hopf bifurcation in [Kuznetsov, 1998] and the bifurcation formulae in [Hassard et al., 1981], we qualitatively analyze the properties for the occurring Hopf bifurcations of the system (3). Finally, an example with numerical simulations is given to illustrate the obtained results.