Journal of Mathematical Chemistry

, Volume 49, Issue 6, pp 1128–1150 | Cite as

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

  • Canrong TianEmail author
Original Paper


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.


Turing patterns Cross-diffusion Nonhomogeneous stationary state 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Basic DepartmentYancheng Institute of TechnologyYanchengChina

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