Calculus of Variations and Geometric Measure Theory

C. Geldhauser - C. Kuehn

Travelling waves in the discrete stochastic Nagumo equation

created by geldhause on 10 Sep 2018



Inserted: 10 sep 2018
Last Updated: 10 sep 2018

Year: 2018


Many physical, chemical and biological systems have an inherent discrete spatial structure that strongly influences their dynamical behaviour. Similar remarks apply to internal or external noise, as well as to nonlocal coupling. In this paper we study the combined effect of nonlocal spatial discretization and stochastic perturbations on travelling waves in the Nagumo equation. We prove that under suitable parameter conditions, various discrete-stochastic variants of the Nagumo equation have solutions, which stay close on long time scales to the classical monotone Nagumo front with high probability if the noise level and spatial discretization are sufficiently small.