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Effort dynamics in a prey-predator model with harvesting. (English) Zbl 1201.91148

Summary: In a fully dynamic model of an open-access fishery, the level of fishing effort expands or contracts according as the net economic revenue to the fishermen is positive or negative. A model reflecting this dynamic interaction between the net economic revenue and the effort in a fishery is called a dynamic reaction model. In the present paper we consider a prey-predator type fishery model with a partial closure of prey species. The steady states of the systems are determined, and the dynamical behavior of both the species is examined. The optimal harvest policy is formulated and solved with the help of Pontryagin’s maximal principle. Results are illustrated with the help of numerical examples.

MSC:

91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
37N40 Dynamical systems in optimization and economics
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