Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent Parameters | Zendy

Changjin Xu | Zendy

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Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent Parameters

Author(s) -

Changjin Xu

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 - 10.1155/2012/264870

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

A class of stage-structured predator-prey model with time delay and delay-dependent parameters is considered. Its linear stability is investigated and Hopf bifurcation is demonstrated. Using normal form theory and center manifold theory, some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained. Finally, numerical simulations are performed to verify the analytical results

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