Biao LIU, Wan-tong LI, Wen-bing XU
This paper investigates the propagation dynamics of nonlocal dispersal cooperative systems within a shifting environment characterized by a contracting favorable region. We examine two distinct types of dispersal kernels. For thin-tailed kernels, we study the existence, uniqueness, and stability of forced waves using upper and lower solutions, the sliding method, and the dynamical systems approach. In the case of partially heavy-tailed kernels, considering compactly supported initial value functions, we demonstrate that for each species, the right side of the level sets exhibits accelerated rightward propagation, while transferability occurs. Conversely, the propagation on the left side does not move leftward but rather rightward, with a spreading speed equivalent to that of the shifting environment. Consequently, species with thin-tailed kernels inherently persist in a shifting habitat, provided they are part of a cooperative and irreducible system that includes at least one species with a heavy-tailed kernel, regardless of the magnitude of the shifting environment's speed. This behavior markedly diverges from the dynamics observed in scalar equations.
