Travelling waves of a three-species Lotka–Volterra food-chain model with spatial diffusion and time delays

This paper is concerned with the existence of travelling wave solutions to a three-species Lotka–Volterra food-chain model with spatial diffusion and time delays. By using the cross iteration method and Schauder’s fixed point theorem, we reduce the existence of travelling wave solutions to the existence of a pair of upper–lower solutions which are easy to construct in practice. Numerical simulations are carried out to illustrate the main results.