EXISTENCE AND STABILITY OF TRAVELING WAVEFRONTS FOR A DISCRETE DIFFUSION SYSTEM WITH NONLOCAL DELAY EFFECTS

This paper is devoted to the study of the existence and stability of traveling wavefronts for a two dimensional discrete diffusion system with nonlocal delay effects. The existence result can be derived by applying the technique of monotone iteration with the help of a pair of explicit upper and lower solutions. Then, using the weighted energy method together with the comparison principle, we prove that the traveling wavefronts with large speed are exponentially stable, when the initial perturbation around the traveling wavefronts decays exponentially as x & RARR; -& INFIN;, but can be arbitrarily large in other locations.