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Optimal taxation policy for a prey-predator fishery model with reserves. (English) Zbl 1371.37146

Summary: This paper is concerned with optimal control problem for a prey-predator fishery model with prey dispersal in two areas, one of which is free fishing area and the other is reserved ares. Selective harvesting effort on prey population is considered. To conserve resource in the exosystem, the regulatory agency manages exploitation of biological resources by imposing a taxation. The existence of its nonnegative equilibria and their qualitative analysis are discussed. The objective is to maximize the monetary economic interests, by virtue of Pontryagin’s maximum principle, the optimal control problem is solved and an optimal taxation policy is obtained to keep the sustainable development of the ecosystem as well as achieve the economic interests of harvesting effort at an ideal level. A simulation example is carried out to show the consistency with the obtained theoretical results.

MSC:

37N35 Dynamical systems in control
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
92D40 Ecology
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