Travelling Waves in Diffusive Leslie–Gower Prey–Predator Model.

In this paper, we mainly study a diffusive Leslie–Gower prey–predator model by the geometric singular perturbation theory. Under assumptions that the diffusion rate of prey is much smaller than that of predator and the natural growth rate of prey is much greater than that of predator, we use dimensionless transformation and traveling wave transformation to transform the diffusive Leslie–Gower prey–predator model into a Multi-scale slow-fast system with two small parameters of different magnitude. According to the Tikhonov–Finichel singular perturbation theory, we analyse the Multi-scale dynamics with respect to two small parameters in turn. Furthermore, we prove the existence of heteroclinic orbit for the slow-fast system. Thus, we get the existence of travelling waves of original reaction-diffusion model. Finally, numerical examples are given to support our theoretical results. [ABSTRACT FROM AUTHOR]