THE MODEL OF FISHERIES MANAGEMENT

At the present stage of development of science, technology and economics, much attention is paid to the development of the mathematical theory of optimal control, since it combines fundamental mathematical developments with actual applied problems. One of such urgent tasks is the conservation and use of natural resources [1]. The aim of the work is to build a mathematical model for fisheries management and to determine the optimal control of this process. The model takes into account the factor of natural birth rate, mortality and other parameters. With the advent of new information, the model is improved and supplemented by new conditions, constraints on the parameters of the problem [2], [3], [4]. The fisheries management is carried out by monitoring the intensity of capture. The goal of management is to maximize profits and preserve the population at a given level [5], [6]. The paper considers a continuous model that takes into account the size (weight) of the population, so that the entire fish population is divided into three age classes, differing in weight and size. In addition, the restriction on market demand is taken into account. The model of fisheries management allows to maximize profit from sale of the catch and to keep a level of a population necessary for the further development. To obtain optimality conditions in the continuous model, the Pontryagin Maximum Principle [5], [7] is used, and in the discrete model approximating the continuous one, the method of rapid automatic differentiation and numerical methods for solving extremal problems [5], [7] are used

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