Coexistence and extinction in the Volterra-Lotka competition model with nonlocal dispersal. (English) Zbl 1264.35113
Summary: Coexistence and extinction for two species Volterra-Lotka competition systems with nonlocal dispersal are investigated. Sufficient conditions in terms of diffusion, reproduction, self-limitation, and competition rates are established for existence, uniqueness, and stability of coexistence states as well as for the extinction of one species. The focus is on environments with hostile surroundings. In this case, our results correspond to those for random dispersal under Dirichlet boundary conditions. Similar results hold for environments with non-flux boundary and for periodic environments, which correspond to those for random dispersal under Neumann boundary conditions and periodic boundary conditions, respectively.
MSC:
35K51 | Initial-boundary value problems for second-order parabolic systems |
47G20 | Integro-differential operators |
47N20 | Applications of operator theory to differential and integral equations |
92D25 | Population dynamics (general) |
92D40 | Ecology |
35K58 | Semilinear parabolic equations |
35R09 | Integro-partial differential equations |
35B50 | Maximum principles in context of PDEs |