Existence of periodic traveling waves in a nonlocal convection–diffusion model with chemotaxis and delay effect

We focus upon the existence of periodic traveling waves in a nonlocal reaction–diffusion model with chemotaxis and nonlocal delay effect. Based on the perturbation method, the existence of periodic traveling waves with large wave speed are obtained by the Lyapunov–Schmidt reduction and the implicit function theorem. The trick of the proof is to treat the wave profile as a solution of an operator in a suitable Banach space.