Math. Model. Nat. Phenom.
Volume 1, Number 1, 2006Population dynamics
|Page(s)||63 - 80|
|Published online||15 May 2008|
Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources
Camille Jordan Institute of Mathematics, UMR 5208 CNRS, University Lyon 1 69622 Villeurbanne, France
2 Institute of Research and Development, 93143 Bondy, France
Corresponding author: email@example.com
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.
Mathematics Subject Classification: 92D15 / 35P15 / 47G20
Key words: integro-differential equations / patterns and waves / evolution
© EDP Sciences, 2006
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