Exponential stability of traveling fronts for a 2D lattice delayed differential equation with global interaction - Shi-Liang Wu (Electronic Journal of Differential Equations, 2013)
The purpose of this paper is to study traveling wave fronts of a two-dimensional (2D) lattice delayed differential equation with global interaction. Applying the comparison principle combined with the technical weighted-energy method, we prove that any given traveling wave front with large speed is time-asymptotically stable when the initial perturbation around the wave front need decay to zero exponentially as $i cosheta +j sinhetao -infty$, where $heta$ is the direction of propagation, but it can be allowed relatively large in other locations. The result essentially extends the stability of traveling wave fronts for local delayed lattice differential equations obtained by Cheng et al [1] and Yu and Ruan [16].