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A model for fishery resource with reserve area. (English) Zbl 1011.92049
Summary: We propose and analyse a mathematical model to study the dynamics of a fishery resource system in an aquatic environment that consists of two zones: a free fishing zone and a reserve zone where fishing is strictly prohibited. Biological and bionomic equilibria of the system are obtained, and criteria for local stability, instability and global stability of the system are derived. It is shown that even if fishery is exploited continuously in the unreserved zone, fish populations can be maintained at an appropriate equilibrium level in the habitat. An optimal harvesting policy is also discussed using Pontryagin’s maximum principle.

92D40 Ecology
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
34D05 Asymptotic properties of solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
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