Deformation of Traveling Waves in Delayed Cellular Neural Networks

In this paper, we establish the existence and describe the global structure of traveling waves for a class of lattice delay differential equations describing cellular neural networks with distributed delayed signal transmission. We describe the transition of wave profiles from monotonicity, damped oscillation, periodicity, unboundedness and back to monotonicity as the wave speed is varied. We also describe an interval of the wave speed where the structure of the wave solution is unknown since the corresponding profile equation involves distributed argument of both advanced and retarded types, and we present some preliminary numerical simulation to illustrate the complexity.