Propagation dynamics of a three-species nonlocal dispersal predator–prey system with two weak competing aborigine preys

Abstract

This paper is concerned with the propagation dynamics of a three-species nonlocal dispersal predator–prey system with two weak competing aborigine preys. Precisely, our main concern is the invading process of an alien predator into the habitat of two aborigine preys, when two preys are weak competitors in the absence of predator. This invasion process can be characterized by the spreading speed of the predator as well as the traveling wave solutions connecting the predator-free state to other states. First, by applying Schauder’s fixed point theorem with the help of two pairs of upper and lower solutions, we prove that there exists a positive number [Formula: see text], when the wave speed is large than or equals to [Formula: see text], the system admits a traveling wave solution connecting the predator-free state to the co-existence state, which indicates the occurrence of invasion-coexistence phenomenon. Then the invading speed of the predator is investigated by using the comparison argument. Our results show that (i) the weak interspecific competition between two preys will not affect the phenomenon of invasive-coexistence; (ii) the invading speed of the predator coincides with the minimal wave speed [Formula: see text].