Bogdanov-Takens Bifurcation in a Leslie-Gower Predator-prey Model with Prey Harvesting  

作　　者：Yi-jun GONG Ji-cai HUANG 

机构地区：[1]School of Mathematics and Statistics,Central China Normal University

出　　处：《Acta Mathematicae Applicatae Sinica》2014年第1期239-244,共6页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.11101170);Research Project of the Central China Normal University(No.CCNU12A01007);the State Scholarship Fund of the China Scholarship Council(2011842509)

摘　　要：This paper discuss the cusp bifurcation of codimension 2 （i.e. Bogdanov-Takens bifurcation） in a Leslie^Gower predator-prey model with prey harvesting, which was not revealed by Zhu and Lan [Phase portraits, Hopf bifurcation and limit cycles of Leslie-Gower predator-prey systems with harvesting rates, Discrete and Continuous Dynamical Systems Series B. 14（1） （2010）, 289-306]. It is shown that there are different parameter values for which the model has a limit cycle or a homoclinic loop.This paper discuss the cusp bifurcation of codimension 2 （i.e. Bogdanov-Takens bifurcation） in a Leslie^Gower predator-prey model with prey harvesting, which was not revealed by Zhu and Lan [Phase portraits, Hopf bifurcation and limit cycles of Leslie-Gower predator-prey systems with harvesting rates, Discrete and Continuous Dynamical Systems Series B. 14（1） （2010）, 289-306]. It is shown that there are different parameter values for which the model has a limit cycle or a homoclinic loop.

关 键 词：Leslie-Gower predator-prey model Bogdanov-Takens bifurcation limit cycle homoclinic loop 

分 类 号：O175[理学—数学]