Uniqueness and stability of traveling waves for cellular neural networks with multiple delays

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 ϕ(n−ct)ϕ(n−ct) with c≤c⁎c≤c⁎ for the cellular neural networks with multiple delays, where c⁎<0c⁎<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