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Turing pattern formation in a predator-prey system with cross diffusion
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2014 (English)In: Applied Mathematical Modelling, ISSN 0307-904X, E-ISSN 1872-8480, Vol. 38, no 21-22, 5022-5032 p.Article in journal (Refereed) Published
Abstract [en]

The paper explores the impacts of cross-diffusion on the formation of spatial patterns in a ratio-dependent predator-prey system with zero-flux boundary conditions. Our results show that under certain conditions, cross-diffusion can trigger the emergence of spatial patterns which is however impossible under the same conditions when cross-diffusion is absent. We give a rigorous proof that the model has at least one spatially heterogenous steady state by means of the Leray-Schauder degree theory. In addition, numerical simulations are performed to visualize the complex spatial patterns.

Place, publisher, year, edition, pages
2014. Vol. 38, no 21-22, 5022-5032 p.
Keyword [en]
Pattern formation, Predator-prey, Cross diffusion
National Category
Mathematical Analysis
URN: urn:nbn:se:umu:diva-97596DOI: 10.1016/j.apm.2014.04.015ISI: 000345182100006OAI: diva2:775131
Available from: 2014-12-30 Created: 2014-12-23 Last updated: 2014-12-30Bibliographically approved

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Zhang, Lai
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