Propagation dynamics in a nonlocal delayed lattice dynamical system with bistable nonlinearity

Abstract

This paper is devoted to the study of wave propagation dynamics for a class of lattice dynamical systems with nonlocal delay and bistable nonlinearity. This problem arises from the propagation phenomenon in biological and physical systems. To understand the propagation phenomenon, we show that all the wave profiles are strictly increasing and are unique up to translation by establishing a series of technical comparison properties of solution. Moreover, we characterize the exact asymptotic behaviors of the wave profiles when they approach the stable steady states by using dynamical system methods.