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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 c∗, when the wave speed is large than or equals to c∗, 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 c∗. [ABSTRACT FROM AUTHOR]

In this paper, we mainly investigate the dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria. We first establish the existence of spreading speed, and show that the spreading speed coincides with the minimal wave speed of traveling wavefronts. Moreover, a lower bound estimate of the spreading speed is given. Then, we prove that the traveling wavefronts with large speeds are globally exponentially stable, when the initial perturbation around the traveling wavefronts decays exponentially as x → − ∞ , but the initial perturbation can be arbitrarily large in other locations. The adopted methods are the weighted energy and the squeezing technique. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the existence and stability of traveling wavefronts for a two dimensional discrete diffusion system with nonlocal delay effects. The existence result can be derived by applying the technique of monotone iteration with the help of a pair of explicit upper and lower solutions. Then, using the weighted energy method together with the comparison principle, we prove that the traveling wavefronts with large speed are exponentially stable, when the initial perturbation around the traveling wavefronts decays exponentially as $ x\rightarrow -\infty $, but can be arbitrarily large in other locations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence and stability of traveling wavefronts for a nonlocal delay Belousov–Zhabotinskii system. We first introduce the new variable and change the two-dimensional system with nonlocal delay into a three-dimensional system without delay. Then the existence of traveling wavefronts is obtained by constructing a pair of suitable super- and sub-solutions and applying Schauder's fixed point theorem. Finally, we establish the exponential stability of traveling wavefronts with large speed by the weighted energy method together with the comparison principle, when the initial perturbation around the traveling wavefront decays exponentially as x → − ∞ , but can be arbitrarily large in other locations. [ABSTRACT FROM AUTHOR]

The purpose of this work is to investigate the existence and stability of traveling wavefronts for a three‐species competitive‐cooperative system with nonlocal dispersal. By applying monotone iteration method combining with a pair of suitable super‐ and sub‐solutions, we establish the existence of traveling wavefronts. The nonexistence of traveling wavefronts is obtained by a contradiction argument. Finally, by using the weighted energy method together with the comparison principle, we prove that the traveling wavefronts with relatively large speeds are exponentially stable as perturbation in some exponentially weighted spaces, when the difference between initial data and traveling wavefronts decays exponentially at negative infinity, but in other locations, the initial data can be very large. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of traveling wavefronts for a three-component Lotka–Volterra system with nonlocal dispersal. This system arises in the study of three-species competition model in which there is no competition between two of these three species. It has been shown that this system admits a bistable traveling wavefront. In this paper, we further investigate the stability of bistable traveling wavefronts. By constructing suitable super- and sub-solutions and using a dynamical system approach, we obtain the globally asymptotic stability of the bistable traveling wavefronts. [ABSTRACT FROM AUTHOR]