Nonlocal dispersal cooperative systems: Acceleration propagation among species

Abstract

We focus on the influences of nonlocal dispersal kernels on the spatial propagation in nonlocal dispersal cooperative systems with initial values having nonempty compact supports. It is well-known that the solution of a monostable nonlocal dispersal scalar equation spreads at a finite speed when the kernel is thin-tailed and propagates by accelerating when the kernel has a heavy tail (the fat-tailed). However, in such systems, we find that one species can propagate by accelerating although its dispersal kernel is thin-tailed, which is a new and interesting phenomenon. More precisely, we show that the spatial propagation of every species at large time is mainly determined by the tail of the maximum of their dispersal kernels, which further implies that their spatial propagation is accelerated by each other because of the cooperation relation between them. This gives us a new understanding of the cooperation relation in the spatial propagation of nonlocal dispersal cooperative systems.