Forced waves of a three species predator-prey system in a shifting environment

Abstract

This paper is concerned with the existence and non-existence of forced waves for a three species predator-prey system in a shifting environment. The speed of these forced waves is the same as the shifting speed of the living environment of these species. We assume that their habitat changes to the hostile environment as time increases. This makes all species go extinction eventually. Under certain conditions on parameters, we obtain two different types (front and mixed front-pulse types) forced waves that connecting different constant states and the extinction state. Moreover, we are able to characterize the minimal shifting speed for each mixed front-pulse type forced waves.