Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays | Zendy

Huitao Zhao | Zendy; Yiping Lin | Zendy; Yunxian Dai | Zendy

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Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays

Author(s) -

Huitao Zhao,

Yiping Lin,

Yunxian Dai

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 - 10.1155/2013/321930

Subject(s) - mathematics , hopf bifurcation , saddle node bifurcation , bifurcation diagram , transcritical bifurcation , stability (learning theory) , pitchfork bifurcation , mathematical analysis , bifurcation , nonlinear system , physics , quantum mechanics , machine learning , computer science

A ratio-dependent predator-prey model with two time delays is studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semitrivial equilibrium is addressed. By using the theory of functional equation and Hopf bifurcation, the conditions on which positive equilibrium exists and the quality of Hopf bifurcation are given. Using a global Hopf bifurcation result of Wu (1998) for functional differential equations, the global existence of the periodic solutions is obtained. Finally, an example for numerical simulations is also included

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