Existence of traveling wave solutions in m-dimensional delayed lattice dynamical systems with competitive quasimonotone and global interaction

Abstract

This paper deals with the existence of traveling wave solutions for m-dimensional delayed lattice dynamical systems with competitive quasimonotone and global interaction. By using Schauder's fixed point theorem and a cross-iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions. The general results obtained will be applied to m-dimensional delayed lattice dynamical systems with Lotka-Volterra type competitive reaction terms and global interaction.