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

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Listed:
  • Weiming Wang
  • Yongli Cai
  • Yanuo Zhu
  • Zhengguang Guo

Abstract

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.

Suggested Citation

  • Weiming Wang & Yongli Cai & Yanuo Zhu & Zhengguang Guo, 2013. "Allee‐Effect‐Induced Instability in a Reaction‐Diffusion Predator‐Prey Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:487810
    DOI: 10.1155/2013/487810
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    References listed on IDEAS

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    1. Fasani, Stefano & Rinaldi, Sergio, 2011. "Factors promoting or inhibiting Turing instability in spatially extended prey–predator systems," Ecological Modelling, Elsevier, vol. 222(18), pages 3449-3452.
    2. Çelik, Canan & Duman, Oktay, 2009. "Allee effect in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1956-1962.
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