Some Qualitative Properties of Traveling Wave Fronts of Nonlocal Diffusive Competition-Cooperation Systems of Three Species with Delays

Abstract

This paper is concerned with nonlocal diffusion systems of three species with delays. By modified version of Ikehara’s theorem, we prove that the traveling wave fronts of such system decay exponentially at negative infinity, and one component of such solutions also decays exponentially at positive infinity. In order to obtain more information of the asymptotic behavior of such solutions at positive infinity, for the special kernels, we discuss the asymptotic behavior of such solutions of such system without delays, via the stable manifold theorem. In addition, by using the sliding method, the strict monotonicity and uniqueness of traveling wave fronts are also obtained.

Existence and stability of traveling wavefronts for a three‐species Lotka–Volterra competitive‐cooperative system with nonlocal dispersal

“…They also obtained that such traveling wavefronts are unique up to translation with the unique wave speed. For the system () with monostable dynamics and delays, Yao et al [19] studied the asymptotic behavior of traveling wavefronts at infinity by modified version of Ikehara's theorem and then established the strict monotonicity and uniqueness of traveling wavefronts by using the sliding method. In this paper, we focus on the existence of monostable traveling wavefronts connecting $$$ {E}_2 $$$ and $$$ {E}_5 $$$, as well as their stability for ().…”