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Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model

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  • Xiaoqin Wang
  • Yongli Cai

Abstract

We present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with cross-diffusion in a Harrison-type predator-prey model. We analyze the global behaviour of the model by establishing a Lyapunov function. We carry out the analytical study in detail and find out the certain conditions for Turing’s instability induced by cross-diffusion. And the numerical results reveal that, on increasing the value of the half capturing saturation constant, the sequences “spots → spot-stripe mixtures → stripes → hole-stripe mixtures → holes” are observed. The results show that the model dynamics exhibits complex pattern replication controlled by the cross-diffusion.

Suggested Citation

  • Xiaoqin Wang & Yongli Cai, 2013. "Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, February.
    • Handle: RePEc:hin:jnlaaa:306467
    DOI: 10.1155/2013/306467
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