Versal unfoldings of predator-prey systems with ratio-dependent functional respons

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:249

Article

Ruan, Shigui¹  Tang, Yilei²  Zhang, Weinian³ 

[1] Univ Miami, Dept Math, Coral Gables, FL 33124 USA

[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[3] Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China

关键词: Predator-prey system;    Versal unfolding;    Normal form;    Degenerate equilibrium;    Heteroclinic loop;    Bifurcation;   

DOI  :  10.1016/j.jde.2010.06.015

来源: Elsevier

【 摘 要 】

In this paper we study the versal unfolding of a predator-prey system with ratio-dependent functional response near a degenerate equilibrium in order to obtain all possible phase portraits for its perturbations. We first construct the unfolding and prove its versality and degeneracy of codimension 2. Then we discuss all its possible bifurcations, including transcritical bifurcation, Hopf bifurcation, and heteroclinic bifurcation, give conditions of parameters for the appearance of closed orbits and heteroclinic loops, and describe the bifurcation curves. Phase portraits for all possible cases are presented. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free