Multiscale methods and survival criteria for diffusive species in striped patterns

Abstract

We analyze mathematical models describing the behavior of populations in spatially heterogeneous environments whose most and least favourable regions for the development of the species alternate in small length scales compared to the dimensions ofrefuge candidate regions. We use homogenization methods and obtain a partial differential equation with constant coefficients. This allows us to study the survival or extinction of a population in a simpler way than performing a direct analysis of the original models in terms of differential equations involving rapidly varying coefficients.