Spreading speeds and travelling waves for non-monotone time-delayed lattice equations

Abstract

A non-monotone time-delayed lattice system with global interaction is considered. The spreading speed, including the upward convergence, is established by comparison arguments and a fluctuation method. The existence of travelling waves is obtained by Schauder;s fixed-point theorem and a limiting process. It turns out that the minimal wave speed of travelling waves coincides with the spreading speed. This journal is © 2010 The Royal Society.