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Prey predator model with asymptotic non-homogeneous predation. (English) Zbl 1253.92049

Summary: We have formulated and analyzed a prey-predator model in a two patch environment (patch 1 and patch 2). Each patch is supposed to be homogeneous. Patch 2 constitutes a reserved area of the prey and no fishing is permitted in this zone whereas patch 1 is an open access fishery zone. The growth of prey in each patch is assumed to be logistic. The transmission function from zone 1 due to predation is considered as a modified function of general nature. Stability analyses along with the optimal harvest policy are also obtained. Numerical simulations have also been performed in support of the analysis. For different values of predation parameter, the equilibrium level has been tabulated. It has been observed that the use of a new transmission function lowers down the equilibrium level.

MSC:

92D40 Ecology
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
37N25 Dynamical systems in biology
34D99 Stability theory for ordinary differential equations
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