Hopf Bifurcations and Oscillatory Patterns of a Homogeneous Reaction-Diffusion Singular Predator-Prey Model | Zendy

Zhenhua Bao | Zendy; He Liu | Zendy

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Hopf Bifurcations and Oscillatory Patterns of a Homogeneous Reaction-Diffusion Singular Predator-Prey Model

Author(s) -

Zhenhua Bao,

He Liu

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 - 10.1155/2013/547425

Subject(s) - mathematics , hopf bifurcation , homogeneous , reaction–diffusion system , predation , mathematical analysis , bifurcation , pitchfork bifurcation , diffusion , boundary (topology) , physics , nonlinear system , thermodynamics , combinatorics , ecology , quantum mechanics , biology

A kind of homogeneous reaction-diffusion singular predator-prey model with no-flux boundary condition is considered. By using the abstract simplified Hopf bifurcation theorem due to Yi et al. 2009, we performed detailed Hopf bifurcation analysis of this particular pattern formation system. These results suggest the existence of oscillatory patterns if the system parameters fall into certain parameter ranges. And all these oscillatory patterns are proved to be unstable

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