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

Ming Zhao | Zendy

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

Author(s) -

Ming Zhao

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/495072

Subject(s) - mathematics , center manifold , hopf bifurcation , stability (learning theory) , functional response , saddle node bifurcation , bifurcation , manifold (fluid mechanics) , period doubling bifurcation , mathematical analysis , predation , control theory (sociology) , predator , nonlinear system , physics , mechanical engineering , paleontology , control (management) , management , quantum mechanics , machine learning , computer science , engineering , economics , biology

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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