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Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption ofResources

Published online by Cambridge University Press:  15 May 2008

S. Genieys*
Affiliation:
Camille Jordan Institute of Mathematics, UMR 5208 CNRS, University Lyon 1 69622 Villeurbanne, France
V. Volpert
Affiliation:
Camille Jordan Institute of Mathematics, UMR 5208 CNRS, University Lyon 1 69622 Villeurbanne, France
P. Auger
Affiliation:
Institute of Research and Development, 93143 Bondy, France
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Abstract

We study a reaction-diffusion equationwith an integral term describing nonlocal consumption of resourcesin population dynamics. We show that a homogeneous equilibrium canlose its stability resulting in appearance of stationary spatialstructures. They can be related to the emergence of biologicalspecies due to the intra-specific competition and randommutations. Various types of travelling waves are observed.

Type
Research Article
Copyright
© EDP Sciences, 2006

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