Isolation effects in a system of two mutually communicating identical patches

Abstract

Starting from the Fisher-Kolmogorov-Petrovskii-Piskunov equation (FKPP) we model the dynamic of a diffusive system with two mutually communicating identical patches and isolated of the remaining matrix. For this system we find the minimal size of each fragment in the explicit form and compare with the explicit results for similar problems found in the literature. From this comparison emerges an unexpected result that for a same set of the parameters, the isolated system studied in this work with size L, can be better or worst than the non isolated systems with the same size L, uniquely depending on the parameter $a_{0}$ (internal conditions of the patches). Due to the fact that this result is unexpected we propose a experimental verification.