Stability of traveling wave solutions for nonlinear cellular neural networks with distributed delays

The purpose of this paper is to study the stability of traveling wave solutions for nonlinear cellular neural networks (CNN) with distributed delays. First, we establish two kinds of comparison theorems for the Cauchy problem of the CNN model. With the help of the comparison theorems, we can show that all solutions of the Cauchy problem for the CNN model converge exponentially to the traveling wave solutions when the initial perturbations around the traveling wave solutions belonging to suitable weighted spaces.