Asymptotic spreading speeds for a predator-prey system with two predators and one prey

TL;DR

This paper analyzes the long-term spreading speeds of a three-species reaction-diffusion system with two predators and one prey, revealing conditions for uniform invasion speeds and complex propagation patterns.

Contribution

It provides a detailed mathematical analysis of the asymptotic spreading speeds in a predator-prey system with mutations and competitive interactions, highlighting nonlocal effects.

Findings

Spreading speed is uniform for mutants when mutations occur.

Multiple propagation layers with different speeds can occur without mutation coupling.

Nonlocal pulling phenomena influence spreading speeds under certain conditions.

Abstract

This paper investigates the large time behaviour of a three species reaction-diffusion system, modelling the spatial invasion of two predators feeding on a single prey species. In addition to the competition for food, the two predators exhibit competitive interactions and under some parameter conditions ($\mu>0$), they can also be considered as two mutants. When mutations occur in the predator populations, the spatial spread of invasion takes place at a definite speed, identical for both mutants. When the two predators are not coupled through mutation, the spreading behaviour exhibits a more complex propagating pattern, including multiple layers with different speeds. In addition, some parameter conditions reveal situations where a nonlocal pulling phenomenon occurs and in particular where the spreading speed is not linearly determined.