Stability of traveling wavefronts in discrete reaction-diffusion equations with nonlocal delay effects

TL;DR

This paper proves the exponential and algebraic stability of traveling wavefronts in discrete reaction-diffusion equations with delay effects, using energy and Green function methods, regardless of delay size.

Contribution

It establishes the stability of wavefronts in delayed discrete reaction-diffusion systems, a novel result for nonlocal delay effects.

Findings

Noncritical wavefronts are globally exponentially stable.

Critical wavefronts are globally algebraically stable.

Stability holds regardless of delay magnitude.

Abstract

This paper deals with traveling wavefronts for temporally delayed, spatially discrete reaction-diffusion equations. Using a combination of the weighted energy method and the Green function technique, we prove that all noncritical wavefronts are globally exponentially stable, and critical wavefronts are globally algebraically stable when the initial perturbations around the wavefront decay to zero exponentially near minus infinity regardless of the magnitude of time delay.