×

zbMATH — the first resource for mathematics

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.

MSC:
92D40 Ecology
35K57 Reaction-diffusion equations
35B40 Asymptotic behavior of solutions to PDEs
35B35 Stability in context of PDEs
PDF BibTeX XML Cite