Bioeconomic dynamics of a fishery modeled as an S-system

A bioeconomic model of a single species fishery is developed by using a realistic catch-rate function and assuming that a regulatory agency controls exploitation of the fishery by imposing a suitable tax on the catch. The existence of a nontrivial steady state and its stability are examined. The optimal harvesting policy is discussed from the viewpoints of variational calculus and control theory. The fishery is then modeled as an S-system by following the recasting techniques of Savageau and Voit. Numerical examples of the optimal control curves and the yield-effort curves are obtained by executing the ESSYNS algorithm.