Traveling waves in a diffusive predator–prey system of Holling type: Point-to-point and point-to-periodic heteroclinic orbits

Abstract

We demonstrate the existence of small amplitude traveling wave train solutions and two kinds of traveling wave solutions of a diffusive predator–prey system with general Holling type functional response, i.e., the analysis shows the existence of periodic orbits, point-to-point connection and point-to-periodic orbit connection. Also, the minimal wave speed for biological invasion is obtained. The method or techniques used here can be extended to a diffusive predator–prey system with more general functional response, not only the Holling type.