Dhar, J. A prey-predator model with diffusion and a supplementary resource for the prey in a two-patch environment. (English) Zbl 1071.92039 Math. Model. Anal. 9, No. 1, 9-24 (2004). 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. Cited in 5 Documents MSC: 92D40 Ecology 35K57 Reaction-diffusion equations 35B40 Asymptotic behavior of solutions to PDEs 35B35 Stability in context of PDEs Keywords:Population diffusion; patchiness; supplementary resource; steady state solution; stability PDF BibTeX XML Cite \textit{J. Dhar}, Math. Model. Anal. 9, No. 1, 9--24 (2004; Zbl 1071.92039)