Open Access
2013 Allee-Effect-Induced Instability in a Reaction-Diffusion Predator-Prey Model
Weiming Wang, Yongli Cai, Yanuo Zhu, Zhengguang Guo
Abstr. Appl. Anal. 2013(SI08): 1-10 (2013). DOI: 10.1155/2013/487810


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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Weiming Wang. Yongli Cai. Yanuo Zhu. Zhengguang Guo. "Allee-Effect-Induced Instability in a Reaction-Diffusion Predator-Prey Model." Abstr. Appl. Anal. 2013 (SI08) 1 - 10, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1272.37038
MathSciNet: MR3039162
Digital Object Identifier: 10.1155/2013/487810

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI08 • 2013
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