A mathematical analysis of a predator-prey system in a highly heterogeneous environment

Abstract

We are concerned with the mathematical analysis of a predator--prey system in heterogeneous domains. We first give a global existence result for the problem with spatially variable coefficients. For highly heterogeneous systems, using homogenization techniques we derive a simpler model with constant coefficients yielding the macroscopic dynamic of the predator--prey system. In this process, standard Lotka--Volterra functional responses to predation are preserved, while Holling type II responses are transformed into unusual nonlocal nonlinearities.