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February  2009, 25(1): 321-342. doi: 10.3934/dcds.2009.25.321

Homogenization and influence of fragmentation in a biological invasion model

Mohammad El Smaily 1, , François Hamel 2, and  Lionel Roques 3,

1. 

Department of Mathematics, University of British Columbia and Pacific Institute for the Mathematical Sciences, 1984 Mathematics Road, V6T 1Z2, Vancouver, BC, Canada
2. 

Aix-Marseille Université, LATP, Faculté des Sciences et Techniques, Avenue Escadrille Normandie-Niemen, F-13397 Marseille Cedex 20
3. 

UR 546 Biostatistique et Processus Spatiaux, INRA, F-84000 Avignon, France

Received  July 2007 Revised  May 2008 Published  June 2009

In this paper, some properties of the minimal speeds of pulsating Fisher-KPP fronts in periodic environments are established. The limit of the speeds at the homogenization limit is proved rigorously. Near this limit, generically, the fronts move faster when the spatial period is enlarged, but the speeds vary only at the second order. The dependence of the speeds on habitat fragmentation is also analyzed in the case of the patch model.
Keywords: Homogenization, pulsating fronts., fragmentation, reaction-diffusion model.
Mathematics Subject Classification: Primary: 35B10, 35B27, 35K57; Secondary: 92B0.
Citation: Mohammad El Smaily, François Hamel, Lionel Roques. Homogenization and influence of fragmentation in a biological invasion model. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 321-342. doi: 10.3934/dcds.2009.25.321
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