A model for fishery resource with reserve area and facing prey-predator interactions. (English) Zbl 1148.92032

The author formulates and analyses a nonlinear 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. This is an important real life problem which addresses ongoing concerns about depletion of aquatic resources. Biological equilibria of the system are obtained, and criteria for local stability and global stability of the system are derived. An optimal harvesting policy is also discussed using Pontryagin’s maximum principle.


92D40 Ecology
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
93D20 Asymptotic stability in control theory