Homogenization and influence of fragmentation in a biological invasion model

Mohammad El Smaily (1) , François Hamel (1) , Lionel Roques (2)

1 Université Paul Cézanne - Aix-Marseille 3
2 BioSP - Biostatistique et Processus Spatiaux

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: FRONT FISHER-KPP; Homogenization; fragmentation; reaction-diffusion model; pulsating fronts

Keywords: BIOLOGICAL INVASION; MODELISATION

Domains: General Mathematics [math.GM]

Mohammad El Smaily, François Hamel, Lionel Roques. Homogenization and influence of fragmentation in a biological invasion model. Discrete and Continuous Dynamical Systems - Series A, 2009, 25 (1), pp.321 - 342. ⟨10.3934/dcds.2009.25.321⟩. ⟨hal-02662379⟩