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Zbl 0634.92017
Beretta, Edoardo; Solimano, Fortunata; Takeuchi, Yasuhiro
Global stability and periodic orbits for two-patch predator-prey diffusion-delay models. (English)
[J] Math. Biosci. 85, 153-183 (1987). ISSN 0025-5564

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.
[R.Bürger]

MSC 2000:: *92D40 Ecology
34C05 Qualitative theory of some special solutions of ODE
34C25 Periodic solutions of ODE
34D99 Stability theory of ODE
92D25 Population dynamics

Keywords: global stability; periodic orbits; two-patch predator-prey diffusion- delay models; Volterra within-patch dynamics; exponential-decay memory function; homotopy techniques; self-regulating coefficient of predator; integrodifferential equations; sufficient conditions for the boundedness of solutions; existence of a nonzero globally stable equilibrium; Hopf bifurcation

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