Stability and Hopf bifurcation analysis of an eco-epidemic model with a stage structure

被引：39
|
作者：
Shi, Xiangyun [2 ]
Cui, Jingan [1 ]
Zhou, Xueyong [2 ,3 ]
机构：
[1] Beijing Univ Civil Engn & Architecture, Sch Sci, Beijing 100044, Peoples R China
[2] Xinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Henan, Peoples R China
[3] Nanjing Normal Univ, Sch Math Sci, Nanjing 210046, Jiangsu, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Eco-epidemiology; Stage structure; Delay; Hopf bifurcation; PREDATOR-PREY SYSTEM; DEPENDENT TIME-DELAY; POPULATION-GROWTH; DISEASE;
D O I：
10.1016/j.na.2010.09.038
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, an eco-epidemiological model with a stage structure is considered. The asymptotical stability of the five equilibria, the existence of stability switches about positive equilibrium, is investigated. It is found that Hopf bifurcation occurs when the delay tau passes though a critical value. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1088 / 1106
页数：19
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