Forced waves for a three-species predator-prey system with nonlocal dispersal in a shifting environment

TL;DR

This paper studies a three-species predator-prey model with nonlocal dispersal in a shifting environment, demonstrating the existence of traveling waves connecting various population states and identifying critical speeds for these waves.

Contribution

It introduces a novel analysis of predator-prey dynamics with nonlocal dispersal in a moving environment, establishing existence results for different wave solutions.

Findings

Existence of waves connecting trivial and coexistence states for any forced speed.

Existence of critical speeds for waves connecting trivial and predator-absent states.

Modeling of population dynamics under climate change-like shifting environments.

Abstract

We consider a three-species predator-prey system involving two competing predators and one prey. The species diffuse with nonlocal dispersal kernels with possibly non-compact support, and they interact in a heterogeneous environment moving with a positive forced speed such that the environment is favorable to the prey in the absence of predators far ahead of the shifting boundary and it is unfavorable far behind. Such systems arise in the modeling of population dynamics under the effect of a shifting environment, such as climate change. We show on the one hand the existence of waves connecting the trivial state to the unique constant positive coexistence state for any value of the forced speed. On the other hand, we show the existence of critical positive speeds for the existence of waves connecting the trivial state to the states corresponding to the absence of one or two predators.