Travelling waves in diffusive Leslie-Gower prey-predator model (Q2670633)

In this paper, authors study a diffusive Leslie-Gower prey-predator model by the geometric singular perturbation theory. Under some assumptions, they 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, authors analyse the multi-scale dynamics with respect to two small parameters in turn and prove the existence of heteroclinic orbit for the slow-fast system. Thus, the existence of travelling waves of original reaction-diffusion model is established. Finally, numerical examples are given to support our theoretical results.