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Global stability and periodic orbits for two-patch predator-prey diffusion-delay models. (English) Zbl 0634.92017
A mathematical model for a one-prey, one-predator system in which the prey can diffuse between one patch with little food and no predation and one patch with much food but with predation is investigated. After transforming the corresponding system of integrodifferential equations into a system of ordinary differential equations, sufficient conditions for the boundedness of solutions and existence of a nonzero globally stable equilibrium are derived. Moreover, it is shown that a Hopf bifurcation may occur if the predator is not self-regulating.
Reviewer: R.Bürger
MSC:
92D40Ecology
34C05Location of integral curves, singular points, limit cycles (ODE)
34C25Periodic solutions of ODE
34D99Stability theory of ODE
92D25Population dynamics (general)