Qualitative properties of traveling waves for nonlinear cellular neural networks with distributed delays

The purpose of this article is to study various qualitative properties of traveling waves for nonlinear cellular neural networks with distributed delays. The existence of monotone traveling waves of the model has been obtained in [25]. In this paper, we first determine the exact asymptotic behavior of the traveling waves at infinity. Then, the non-existence of the traveling waves is established. Finally, based on a strong comparison theorem, we prove the monotonicity and uniqueness (up to translation) of the traveling waves.