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Nonlocal interaction driven pattern formation in a prey-predator model
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2017 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 308, 73-83 p.Article in journal (Refereed) Published
Abstract [en]

A widely observed scenario in ecological systems is that populations interact not only with those living in the same spatial location but also with those in spatially adjacent locations, a phenomenon called nonlocal interaction. In this paper, we explore the role of nonlocal interaction in the emergence of spatial patterns in a prey-predator model under the reaction-diffusion framework, which is described by two coupled integro-differential equations. We first prove the existence and uniqueness of the global solution by means of the contraction mapping theory and then conduct stability analysis of the positive equilibrium. We find that nonlocal interaction can induce Turing bifurcation and drive the formation of stationary spatial patterns. Finally we carry out numerical simulations to demonstrate our analytical findings.

Place, publisher, year, edition, pages
2017. Vol. 308, 73-83 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-134685DOI: 10.1016/j.amc.2017.03.017ISI: 000399591500006OAI: oai:DiVA.org:umu-134685DiVA: diva2:1114098
Available from: 2017-06-22 Created: 2017-06-22 Last updated: 2017-06-22Bibliographically approved

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Zhang, Lai
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CiteExportLink to record
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  • apa
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