Homogenization and influence of fragmentation in a biological invasion model

Mohammad El Smaily; François Hamel; Lionel Roques

doi:10.3934/dcds.2009.25.321

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2009, Volume 25, Issue 1: 321-342. Doi: 10.3934/dcds.2009.25.321

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Homogenization and influence of fragmentation in a biological invasion model

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

Received: June 30, 2007

Revised: April 30, 2008

Published: December 2008

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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.

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Mathematics Subject Classification: Primary: 35B10, 35B27, 35K57; Secondary: 92B05.

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