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

Xiaoqin Wang and Yongli Cai

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

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.

Date: 2013
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https://doi.org/10.1155/2013/306467

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:306467

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