Stability of Traveling Waves Solutions for Nonlinear Cellular Neural Networks with Distributed Delays

This paper investigates the exponential stability of traveling wave solutions for nonlinear delayed cellular neural networks. As a continuity of the past work (Wu and Niu, 2016; Yu,et al., 2011) on the existence and uniqueness of the traveling wave solutions, it is very reasonable and interesting to consider the exponential stability of the traveling wave solutions. By the weighted energy method, comparison principle and the first integral mean value theorem, this paper proves that, for all monotone traveling waves with the wave speed c < c(1)* < 0 or c > c(2)* > 0, the solutions converge time-exponentially to the corresponding traveling waves, when the initial perturbations decay at some fields.

Automated summary

This paper investigates the exponential stability of traveling wave solutions for nonlinear delayed cellular neural networks. Through the weighted energy method, comparison principle, and the first integral mean value theorem, it is proven that solutions converge time-exponentially to the corresponding traveling waves under certain conditions.