Renewable resource management in a seasonally fluctuating environment with restricted harvesting effort

Abstract

This paper presents bio-economics of a renewable resources in a seasonally changing environment in which the resource exploitation is subjected to restrictions on harvesting effort. The dynamics of the resource is assumed to be governed by the logistic equation. Seasonality is incorporated into the system by choosing the coefficients in the growth equation to be periodic functions with the same period. A linear optimal control problem involving binding constraints on the control variable has been considered. As a result the concept of blocked interval plays a key role in the construction of optimal solution. In view of the periodicity associated with the considered problem, we first construct an optimal periodic solution. The optimal solution is established using the most rapid approach path to the said optimal periodic solution. The global asymptotic stability property of the optimal periodic solution enables construction of a suboptimal solution. The optimal solution is found to be periodic after some finite time and suboptimal solution approaches the optimal periodic solution asymptotically. Key results are illustrated through numerical simulation.