Environment fluctuations on single species pattern formation

TL;DR

This paper investigates how environmental fluctuations modeled as Gaussian white noise influence pattern formation and stability in a stochastic nonlocal Fisher-KPP equation, combining analytical and numerical methods.

Contribution

It introduces a stochastic generalization of the nonlocal Fisher-KPP equation incorporating environmental noise and analyzes its effects on pattern stability and coherence.

Findings

Noise can induce coherence in pattern formation.

Environmental fluctuations affect the stability of patterns.

Analytical and numerical results show noise impacts on dispersion relation and structure function.

Abstract

System-environment interactions are intrinsically nonlinear and dependent on the interplay between many degrees of freedom. The complexity may be even more pronounced when one aims to describe biologically motivated systems. In that case, it is useful to resort to simplified models relying on effective stochastic equations. A natural consideration is to assume that there is a noisy contribution from the environment, such that the parameters which characterize it are not constant but instead fluctuate around their characteristic values. From this perspective, we propose a stochastic generalization of the nonlocal Fisher-KPP equation where, as a first step, environmental fluctuations are Gaussian white noises, both in space and time. We apply analytical and numerical techniques to study how noise affects stability and pattern formation in this context. Particularly, we investigate noise induced coherence by means of the complementary information provided by the dispersion relation and the structure function.