Travelling wavefronts in the diffusive single species model with Allee effect and distributed delay

Abstract

In this paper, we consider the diffusive single species model with Allee effect and distributed delay time. Special attention is paid to the existence of travelling wavefront solutions. First, we shall show that such fronts exist when the convolution kernel assumes the strong generic delay kernel and the delay is sufficiently small. Then, in the non-local spatial terms which account for the drift of individuals to their present position from their possible positions at previous times, we shall show that such fronts still exist for the weak generic delay kernel and small delay. The approach used in this paper is the geometric singular perturbation theory.