Stability and Hopf bifurcation analysis of a predator-prey system with diffusion and two delays

Author

Yu, Futian ; Jiang, Minghui ; Shen, Yanjun ; Yuan, Weirong

Author_Institution

Inst. of Nonlinear Complex Syst., China Three Gorges Univ., Yichang, China

fYear

2012

fDate

23-25 March 2012

Firstpage

35

Lastpage

42

Abstract

In this paper, a predator-prey system with diffusion and two delays is investigated. By analyzing the characteristic equations, the local stability of positive equilibrium and local Hopf bifurcations is discussed. Moreover, some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions are obtained by using normal form theory and center manifold theory. The results we obtain can be used to provide reliable foundation for making control strategy.

Keywords

bifurcation; delays; diffusion; predator-prey systems; stability; Hopf bifurcation periodic solution; center manifold theory; control strategy; delays; diffusion; explicit formula; local Hopf bifurcation analysis; local stability; normal form theory; positive equilibrium; predator-prey system; Asymptotic stability; Bifurcation; Delay effects; Manifolds; Predator prey systems; Stability analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Science and Technology (ICIST), 2012 International Conference on

Conference_Location

Hubei

Print_ISBN

978-1-4577-0343-0

Type

conf

DOI

10.1109/ICIST.2012.6221604

Filename

6221604