A classification of the possible long-time behaviors of a two-species cooperative (mutualistic) population model with nonlocal (convolution-kernel) diffusion and moving free boundaries. Because the cooperative coupling is reducible, the system admits many non-constant nonnegative steady states, yielding richer outcomes than the irreducible monostable case; the analysis also gives the spreading speeds of the free boundaries, the limiting states of the two populations, and threshold conditions on the dispersal kernels under which spreading accelerates.
Studies the long-time dynamics of a two-species population model in which each species disperses by nonlocal diffusion (movement governed by a convolution kernel rather than a Laplacian) and each occ…