Travelling fronts in the diffusive Nicholson's blowflies equation with distributed delays

Abstract

We consider the diffusive Nicholson's blowflies equation where the time delay is of the distributed kind, incorporated as an integral convolution in time. Of interest is the question of the existence of travelling front solutions and their qualitative form. For small delay, existence of such fronts is proved when the convolution kernel assumes a special form, enabling the use of linear chain techniques. The resulting higher-dimensional system is studied using geometric singular perturbation theory. The method should be applicable to other such kernels as well. For larger delays, numerical simulations show that the main effect is a loss of monotonicity of the wave front.