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

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 condition, 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.

Asymptotic speed of spread for a nonlocal evolutionary-epidemic system

“…We refer the reader to [4,6,9,12,14,18,19,25] for system with local diffusion, to [7,28] for non-monotone systems with nonlocal diffusion. We also refer to [5,26] for studies of the spreading behaviour for three interacting (competitive coupled with predator-prey interactions) species.…”

“…In this note, our spreading speed analysis extends to nonlocal diffusion some dynamical system ideas used in [4,5,6] for systems with local diffusion to overcome the lack of comparison principle. More specifically our analysis is mostly based on ideas coming from the uniform persistence theory for semiflows, for which we refer the reader to [13,16,23] and the references cited therein.…”

Persistence of species in a predator-prey system with climate change and either nonlocal or local dispersal

“…The main idea of the proof of Theorem 2.7 is motivated by a method used in [14,15] which is different from that for the proof of Theorems 2.5 and 2.6. It strongly relies on parabolic estimates and the compactness of the set of solutions with bounded initial data, which is a much more difficult issue in the nonlocal diffusion framework.…”

“…Survival of the prey. Our proof is inspired by the methods in [14,15]. The first step is to investigate the supremum limit of solutions in the intermediate moving frames.…”

Traveling Wave Solutions for Some Three-Species Predator-Prey Systems

“…This is done by applying some dynamical system arguments from persistence theory (cf. [8,7]). Actually, this very technical part is one of the main contributions of the work [3].…”