Geodesic
Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources
S. Genieys1 ; V. Volpert1 ; P. Auger2
1 Camille Jordan Institute of Mathematics, UMR 5208 CNRS, University Lyon 1 69622 Villeurbanne, France
2 Institute of Research and Development, 93143 Bondy, France
Mathematical modelling of natural phenomena, Tome 1 (2006) no. 1, pp. 63-80.

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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.
DOI : 10.1051/mmnp:2006004

S. Genieys 1 ; V. Volpert 1 ; P. Auger 2

1 Camille Jordan Institute of Mathematics, UMR 5208 CNRS, University Lyon 1 69622 Villeurbanne, France
2 Institute of Research and Development, 93143 Bondy, France 
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S. Genieys; V. Volpert; P. Auger. Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources. Mathematical modelling of natural phenomena, Tome 1 (2006) no. 1, pp. 63-80. doi : 10.1051/mmnp:2006004. http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2006004/

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