Isolation effects in a system of two mutually communicating identical patches

TL;DR

This paper models a diffusive system with two isolated patches using FKPP equations, revealing that isolation can either improve or worsen system behavior depending on internal parameters, which is counterintuitive and warrants experimental validation.

Contribution

It provides explicit formulas for the minimal size of patches in an isolated system and uncovers unexpected effects of isolation depending on internal parameters.

Findings

Isolation can improve or worsen system performance based on internal parameters.

Explicit formulas for minimal patch size in isolated systems are derived.

Unexpected effects of isolation are identified, prompting experimental verification.

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.