Propagation dynamics of a three-species predator-prey model with non-local dispersal in a shifting habitat

This paper is concerned with the propagation phenomenon of a non-local dispersal predator-prey system involving two preys and one predator in a shifting habitat. Assuming that the growth rate of each prey is moving to the right at a speed of s and the habitat is suitable for each prey to survive before the shifting edge, while the habitat behind the boundary is not suitable for survival. For any given speed of the shifting habitat edge, we establish four types of forced extinction waves, which describe the conversion from the state of a saturated aboriginal prey with a pair of invading alien predator-prey, two aboriginal co-existent preys with an invading alien predator, a pair of aboriginal co-existent predator-prey and an invading alien prey, and the co-existence of three species to the extinction state, respectively. Meanwhile, we show the non-existence of some forced waves.