Uniqueness and stability of traveling waves for cellular neural networks with multiple delays
Abstract In this paper, we investigate the properties of traveling waves to a class of lattice differential equations for cellular neural networks with multiple delays. Following the previous study [38] on the existence of the traveling waves, here we focus on the uniqueness and the stability of these traveling waves. First of all, by establishing the a priori asymptotic behavior of traveling waves and applying Ikehara's theorem, we prove the uniqueness (up to translation) of traveling waves ph n c t with c c for the cellular neural networks with multiple delays, where c 0 is the critical wave speed. Then, by the weighted energy method together with the squeezing technique, we further show the global stability of all non critical traveling waves for this model, that is, for all monotone waves with the speed c c the original lattice solutions converge time exponentially to the corresponding traveling waves, when the initial perturbations around the monotone traveling waves decay exponentially at far fields, but can be arbitrarily large in other locations.