Periodic traveling waves in a reaction-diffusion model with chemotaxis and nonlocal delay effect

In this paper, we study the existence of periodic traveling wave solutions with large wave speed for a reaction-diffusion model with chemotaxis and nonlocal delay effect by applying the perturbation method. The proof relies on an abstract formulation of the wave profile as a solution of an operator equation in a certain Banach space, coupled with the Lyapunov-Schmidt reduction and the implicit function theorem.