Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion | Zendy

Xinze Lian | Zendy; Shuling Yan | Zendy; Hailing Wang | Zendy

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Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion

Author(s) -

Xinze Lian,

Shuling Yan,

Hailing Wang

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 - 10.1155/2013/147232

Subject(s) - pattern formation , diffusion , mathematics , predation , turing , replication (statistics) , hopf bifurcation , dynamics (music) , stability (learning theory) , statistical physics , instability , ecology , statistics , physics , computer science , bifurcation , biology , mechanics , genetics , nonlinear system , quantum mechanics , machine learning , acoustics , programming language , thermodynamics

We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation

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