No abstract

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.

This paper is concerned with the propagation dynamics of a discrete diffusive equation with non‐local delay. First of all, by exploring the asymptotic behavior of the solution of the upper system corresponding to the perturbation equation, we obtain the global stability of semi‐wavefronts. It is noteworthy that the kernel function can be asymmetric (i.e., ). Secondly, we estimate the level set of the equation on the basis of the above stability. In particular, the results show that the solution of the compact supported initial value problem is not persistent in special case.