Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Homogenization and influence of fragmentation in a biological invasion model

Pages: 321 - 342, Volume 25, Issue 1, September 2009      doi:10.3934/dcds.2009.25.321

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Mohammad El Smaily - Department of Mathematics, University of British Columbia and Pacific Institute for the Mathematical Sciences, 1984 Mathematics Road, V6T 1Z2, Vancouver, BC, Canada (email)
François Hamel - Aix-Marseille Université, LATP, Faculté des Sciences et Techniques, Avenue Escadrille Normandie-Niemen, F-13397 Marseille Cedex 20, France (email)
Lionel Roques - UR 546 Biostatistique et Processus Spatiaux, INRA, F-84000 Avignon, France (email)

Abstract: 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, fragmentation, reaction-diffusion model, pulsating fronts.
Mathematics Subject Classification:  Primary: 35B10, 35B27, 35K57; Secondary: 92B05.

Received: July 2007;      Revised: May 2008;      Available Online: June 2009.