Population diffusion in a two-patch environment. (English) Zbl 0672.92021

Summary: A model of a single-species population diffusing in a two-patch environment is proposed. It is shown that there exists a positive, monotonic, continuous steady-state solution with continuous flux, in the cases of both reservoir and no-flux boundary conditions, that is asymptotically stable. In the case of patches with equal carrying capacities, it is shown that the uniform steady state is globally asymptotically stable.


92D40 Ecology
35Q99 Partial differential equations of mathematical physics and other areas of application
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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