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A prey-predator model with diffusion and a supplementary resource for the prey in a two-patch environment. (English) Zbl 1071.92039
Summary: A prey-predator dynamics, where the predator species partially depends upon the prey species in a two patch habitat with diffusion and there is a non-diffusing additional resource for the prey population, is modeled and analyzed. It is shown, that there exists a positive, monotonic, continuous steady state solution with continuous matching at the interface for both species separately. Further, we obtain conditions for asymptotic stability for both linear and nonlinear cases.

92D40 Ecology
35K57 Reaction-diffusion equations
35B40 Asymptotic behavior of solutions to PDEs
35B35 Stability in context of PDEs