Traveling wavefronts in diffusive and cooperative Lotka–Volterra system with delays

Abstract

Existence of traveling wave front solutions is established for diffusive and cooperative Lotka–Volterra system with delays. The result is an extension of an existing result for delayed logistic scaler equation to systems, and is somewhat parallel to the existing result for diffusive and competitive Lotka–Volterra systems without delay. The approach used in this paper is the upper–lower solution technique and the monotone iteration recently developed by Wu and Zou (J. Dynam. Differential Equations 13 (2001) 651–687) for delayed reaction–diffusion systems without the so-called quasimonotonicity.