Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay | Zendy

Shuang Guo | Zendy; Weihua Jiang | Zendy

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Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay

Author(s) -

Shuang Guo,

Weihua Jiang

Publication year - 2012

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 - 10.1155/2012/363051

Subject(s) - mathematics , center manifold , hopf bifurcation , type (biology) , stability (learning theory) , bifurcation , polynomial , manifold (fluid mechanics) , mathematical analysis , nonlinear system , mechanical engineering , ecology , physics , quantum mechanics , machine learning , computer science , engineering , biology

A class of three-dimensional Gause-type predator-prey model with delay is considered. Firstly, a group of sufficient conditions for the existence of Hopf bifurcation is obtained via employing the polynomial theorem by analyzing the distribution of the roots of the associated characteristic equation. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by applying the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the obtained results

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