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Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays

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  • Ming Zhao

Abstract

This paper is concerned with a semiratio-dependent predator-prey system with nonmonotonic functional response and two delays. It is shown that the positive equilibrium of the system is locally asymptotically stable when the time delay is small enough. Change of stability of the positive equilibrium will cause bifurcating periodic solutions as the time delay passes through a sequence of critical values. The properties of Hopf bifurcation such as direction and stability are determined by using the normal form method and center manifold theorem. Numerical simulations confirm our theoretical findings.

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  • Ming Zhao, 2013. "Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-13, September.
    • Handle: RePEc:hin:jnlaaa:495072
    DOI: 10.1155/2013/495072
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