Aplikasi kontrol optimum pada pemanenan Sardinella lemuru di Selat Bali

Abstract

This paper studied a mathematical model of fishery resource dynamics in an aquatic area. The considered area consists of two zones: reserve and unreserve zones, where growth of fish population on each zone is given by a nonlinear differential equation. The stability of two nonnegative fixed points are investigated by solving characteristic equation. The fixed points are saddle and stable node. More over, an optimal harvesting policy is analyzed by using Pontryagin maximum principle, from which the bang-bang and singular controls are found as optimal controls. An illustrative example is provided by considering the harvesting of Sardinella lemuru in Bali Strait. This case is simulated numerically by using fourth-order Runge-Kutta method, from which fishery resource dynamics in two zones under optimal harvesting are illustrated.