Spatial invasion dynamics for a time period predator‐prey system

Abstract

This paper is concerned with the propagation theory of a predator‐prey system in a periodic environment. We consider the invasion process that the prey is the aboriginal, whereas the predator is the invader. If the initial habitat size of the predator is finite, then the asymptotic speed of spreading of the predator is given. Furthermore, the existence and nonexistence of traveling wave solutions are obtained, which defined a minimal wave speed of traveling wave solutions. Our results imply that the minimal wave speed of traveling wave solutions is equal to the asymptotic speed of spreading of the predator.