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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 ,
V. Volpert  and
P. Auger
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
*
genieys@math.univ-lyon1.fr
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Abstract

We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources in population dynamics. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. They can be related to the emergence of biological species due to the intra-specific competition and random mutations. Various types of travelling waves are observed.

Keywords

integro-differential equationspatterns and wavesevolution
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 1 , Issue 1: Population dynamics , 2006 , pp. 63 - 80
Copyright
© EDP Sciences, 2006

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