Bifurcation of an eco-epidemiological model with a nonlinear incidence rate

被引：16
|
作者：
Liu, Xuanliang [1 ]
机构：
[1] S China Univ Technol, Sch Math Sci, Guangzhou 510640, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 218卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Predator-prey system; Nonlinear incidence rate; Limit cycle; Hopf bifurcation; Bogdanov-Takens bifurcation; PREDATOR-PREY MODEL; BEHAVIOR; DISEASE;
D O I：
10.1016/j.amc.2011.07.050
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A predator-prey system with disease in the prey is considered. Assume that the incidence rate is nonlinear, we analyse the boundedness of solutions and local stability of equilibria, by using bifurcation methods and techniques, we study Bogdanov-Takens bifurcation near a boundary equilibrium, and obtain a saddle-node bifurcation curve, a Hopf bifurcation curve and a homoclinic bifurcation curve. The Hopf bifurcation and generalized Hopf bifurcation near the positive equilibrium is analyzed, one or two limit cycles is also discussed. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：2300 / 2309
页数：10
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