Analyses of Bifurcations and Stability in a Predator-prey System with Holling Type-Ⅳ Functional Response

被引：15

作者：

Ji-cai Huang~1 Dong-mei Xiao~21 Academy of Mathematics and Systems Science

机构：

来源：

Acta Mathematicae Applicatae Sinica(English Series) | 2004年 / 01期

关键词：

Predator-prey system; Limit cycle; Bogdanov-Takens bifurcation;

D O I：

暂无

中图分类号：

Q141 [数学生态学与生物模型];

学科分类号：

0701 ; 070104 ;

摘要：

In this paper the dynamical behaviors of a predator-prey system with Holling Type-Ⅳfunctionalresponse are investigated in detail by using the analyses of qualitative method,bifurcation theory,and numericalsimulation.The qualitative analyses and numerical simulation for the model indicate that it has a unique stablelimit cycle.The bifurcation analyses of the system exhibit static and dynamical bifurcations including saddle-node bifurcation,Hopf bifurcation,homoclinic bifurcation and bifurcation of cusp-type with codimension two(ie,the Bogdanov-Takens bifurcation),and we show the existence of codimension three degenerated equilibriumand the existence of homoclinic orbit by using numerical simulation.

引用

页码：169 / 180

页数：12