Traveling wave solutions in a modified Leslie–Gower model with diffusion and chemotaxis

In this paper, we study the existence and minimal wave speed of traveling wavefronts and the existence of periodic waves for a modified Leslie–Gower model with diffusion and chemotaxis. The existence of traveling wavefronts is proved by applying the perturbation method. Our approach is based on an abstract formulation of the wave profile as a solution of an operational equation in a certain Banach space, coupled with the Fredholm theory and the Banach contraction mapping principle. Moreover, we study the minimal wave speed of traveling wavefronts by using the standard stability analysis, and investigate the existence condition of periodic waves when traveling wavefronts disappears. Some numerical simulations are presented to illustrate our main results.