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Turing patterns created by cross-diffusion for a Holling II and Leslie-Gower type three species food chain model

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Abstract

In this paper, we develop a theoretical framework for a research into spatial patterns in a three-species Holling II and Leslie-Gower type food chain model with cross-diffusion, the results of which show that the cross-diffusion induces the spatial patterns. When biological pattern formation has been concerned with the method of reaction-diffusion theory, in most of the previous works, as a precondition, the assumption of the existence of nonhomogeneous steady state is presented essentially. We give a rigorous proof to the assumption that the model has at least a nonhomogeneous stationary solution by the Leray-Schauder degree theory. Moreover, the numerical simulations for spatial pattern is also carried out, we propose a method to estimate the wavenumber of the spatial patterns.

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Authors and Affiliations

  1. Basic Department, Yancheng Institute of Technology, Yancheng, 224003, China

    Canrong Tian

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  1. Canrong Tian
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Correspondence to Canrong Tian.

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The work is partially supported by PRC grant NSFC 10801115.

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Tian, C. Turing patterns created by cross-diffusion for a Holling II and Leslie-Gower type three species food chain model. J Math Chem 49, 1128–1150 (2011). https://doi.org/10.1007/s10910-011-9801-z

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  • DOI: https://doi.org/10.1007/s10910-011-9801-z

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