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

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 b...

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Bibliographic Details
Main Authors: Futian Yu, Minghui Jiang, Yanjun Shen, Weirong Yuan
Format: Conference Proceeding
Language:English
Subjects:
Asymptotic stability
Bifurcation
Delay effects
Manifolds
Predator prey systems
Stability analysis
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Summary: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.
ISSN:2164-4357
DOI:10.1109/ICIST.2012.6221604