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

Xiaoqin Wang | Zendy; Yongli Cai | Zendy

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

Author(s) -

Xiaoqin Wang,

Yongli Cai

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 - 10.1155/2013/306467

Subject(s) - instability , diffusion , statistical physics , pattern formation , saturation (graph theory) , reaction–diffusion system , turing , mathematics , population , lyapunov function , constant (computer programming) , replication (statistics) , predation , mathematical analysis , physics , statistics , mechanics , computer science , ecology , nonlinear system , biology , thermodynamics , demography , combinatorics , quantum mechanics , sociology , genetics , programming language

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

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