Travelling wavefronts in delayed lattice dynamical systems with global interaction

Abstract

This paper is concerned with the travelling wavefronts of delayed lattice dynamical systems with global interaction. We establish the existence of the travelling wavefronts by upper–lower solutions technique and Schauder's fixed point theorem when the system satisfies the quasimonotone condition. The nonexistence of the travelling wavefronts of the system is considered by the comparison principle and the corresponding results of the scalar equation. Finally, we apply our main results to the Logistic model and Belousov–Zhabotinskii system on lattice. Our main finding here is that the global interaction can increase the minimal wave speed while the delay can decrease it.