Monostable traveling waves for a time-periodic and delayed nonlocal reaction–diffusion equation

Abstract

This paper is concerned with a time-periodic and delayed nonlocal reaction–diffusion population model with monostable nonlinearity. Under quasi-monotone or non-quasi-monotone assumptions, it is known that there exists a critical wave speed \(c_*>0\) such that a periodic traveling wave exists if and only if the wave speed is above \(c_*\). In this paper, we first prove the uniqueness of non-critical periodic traveling waves regardless of whether the model is quasi-monotone or not. Further, in the quasi-monotone case, we establish the exponential stability of non-critical periodic traveling fronts. Finally, we illustrate the main results by discussing two types of death and birth functions arising from population biology.