Depinning transitions in discrete reaction-diffusion equations

TL;DR

This paper investigates the conditions under which wave fronts in discrete reaction-diffusion systems become pinned or propagate, analyzing the depinning transition and providing criteria for propagation failure.

Contribution

It offers a detailed analysis of the depinning transition in discrete bistable reaction-diffusion equations, including conditions for front pinning and an approximation for the wave speed near the threshold.

Findings

Identification of critical parameters for depinning transition

Conditions for front pinning and propagation failure

Approximate wave speed beyond the depinning threshold

Abstract

We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of traveling waves to steady solutions near threshold and give conditions for front pinning (propagation failure). The critical parameter values are characterized at the depinning transition and an approximation for the front speed just beyond threshold is given.