Delayed Metapopulation models with general dispersion matrix and nonlocal interactions

This paper provides sharp criteria of local and global attraction for classical metapopulation models. Our analysis allows any arrangement of patches, nonlocal effects, and bistable nonlinearities. To our knowledge, this is the first general methodology for handling nonautonomous metapopulation models with bistable nonlinearities. From a biological perspective, we review some classical results in metapopulation theory when nonlocal effects are included. The conclusion is that the interplay between diffusion and nonlocal effects generates new dynamical behaviors.