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Traveling wave governs the stability of spatial pattern in a model of allelopathic competition interactions
Department of Basic Sciences, Yancheng Institute of Technology, Yancheng 224003, China .
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2012 (English)In: Chaos, ISSN 1054-1500, E-ISSN 1089-7682, Vol. 22, no 4, 043136- p.Article in journal (Refereed) Published
Abstract [en]

Inhomogenous distribution of populations across physical space is a widely observed scenario in nature and has been studied extensively. Mechanisms accounting for these observations are such as diffusion-driven instability and mechanochemical approach. While conditions have been derived from a variety of models in biological, physical, and chemical systems to trigger the emergence of spatial patterns, it remains poorly understood whether the spatial pattern possesses asymptotical stability. In a plankton allelopathic competitive system with distributed time delay, we found that spatial pattern arises as a result of Hopf bifurcation and, in the meantime, there exists a unique asymptotically stable traveling wave solution. The convergence of the traveling wave solution to the emergent pattern and its stability infer that the emergent spatial pattern is locally asymptotically stable.

Place, publisher, year, edition, pages
2012. Vol. 22, no 4, 043136- p.
Keyword [en]
asymptotic stability, bifurcation, delays, diffusion, microorganisms, pattern formation, wave propagation
National Category
URN: urn:nbn:se:umu:diva-64962DOI: 10.1063/1.4770064ISI: 000312831600036OAI: diva2:608097
Available from: 2013-02-26 Created: 2013-02-04 Last updated: 2013-02-26Bibliographically approved

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Zhang, Lai
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