Allee-Effect-Induced Instability in a Reaction-Diffusion Predator-Prey Model | Zendy

Weiming Wang | Zendy; Yongli Cai | Zendy; Yanuo Zhu | Zendy; Zhengguang Guo | Zendy

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Allee-Effect-Induced Instability in a Reaction-Diffusion Predator-Prey Model

Author(s) -

Weiming Wang,

Yongli Cai,

Yanuo Zhu,

Zhengguang Guo

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 - 10.1155/2013/487810

Subject(s) - allee effect , diffusion , instability , reaction–diffusion system , predation , statistical physics , physics , ecology , biology , mechanics , population , thermodynamics , demography , sociology

We investigate the spatiotemporal dynamics induced by Allee effect in a reaction-diffusion predator-prey model. In the case without Allee effect, there is nonexistence of diffusion-driven instability for the model. And in the case with Allee effect, the positive equilibrium may be unstable under certain conditions. This instability is induced by Allee effect and diffusion together. Furthermore, via numerical simulations, the model dynamics exhibits both Allee effect and diffusion controlled pattern formation growth to holes, stripes-holes mixture, stripes, stripes-spots mixture, and spots replication, which shows that the dynamics of the model with Allee effect is not simple, but rich and complex

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