Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions

Abstract

This work investigates traveling waves for a class of delayed cellular neural networks with nonmonotonic output functions on the one-dimensional integer lattice $\mathbb{Z}$. The dynamics of each given cell depends on itself and its nearest $m$ left or $l$ right neighborhood cells with distributed delay due to, for example, finite switching speed and finite velocity of signal transmission. Our technique is to construct two appropriate nondecreasing functions to squeeze the nonmonotonic output functions. Then we construct a suitable wave profiles set and derive the existence of traveling wave solutions by using Schauder's fixed point theorem.