The Optimal Control Problem Of Three Classes Of Inshore-offshore Fishery System With Harvest

In this paper, three classes of inshore-offshore fishery model with harvesting are studied through applying the differential system and the basic theory of population dynamics and extremum principle of maximum principle. The results of the study has a certain practical significance.The main research contents and results in this thesis are as follows:(1) The dynamic behavior and optimal control problem of a class of inshore-offshore fishery model with proportional harvesting is studied.The system is consid-ered with periodic coefficients and impulsive diffusion between inshore subpopulation and offshore subpopulation. The conditions for existence and stability of periodic solutions are obtained. Moreover, when the parameters are constants, the optimal control is obtained through applying analytical skills; when the parameters are pe-riodic functions, the optimal control is obtained through applying the maximum principle of impulsive differential systems, the purpose is to control the harvesting effort as to maximize the profit which is the difference between economic revenue and cost.(2) A class of inshore-offshore fishery model with impulsive harvesting and periodic coefficients is considered, the dynamic behavior and optimal harvesting policy are investigated. The inshore fish and offshore fish diffuse with each other at the fixed moment, and the inshore fish is harvested immediately for economic profit after the diffusion. Applying the basic theory of impulsive differential system and some analytic techniques, we obtain the condition which ensures the existence and stability of positive periodic solution. The purpose is to control the harvesting effort so as to maximize the profit which is the difference between economic revenue and cost. The exact expression of the optimal control strategy is obtained.(3) The dynamic behavior and optimal harvesting policy for a class of inshore-offshore fishery model are investigated. In the model, the inshore fish is harvested simultaneously with linear harvest function, and the inshore fish and offshore fish diffuse with each other continuously. Objective functional is to obtain the maximal profit which is the difference between economic revenue and cost. The optimal control policy is obtained through applying Pontryagin maximum principle and some analytic skills, the exact expressions of optimization policy and the economic profit are given.