Dynamic Analysis And Optimal Control Of Several Fishery Economic Models

In this thesis,the dynamic behavior and optimal control problem of a single-species fishery economic model are investigated.The establishment of the model is based on the logistic equation,considering that the catch rate is affected by the total revenue and the total cost,the unit price of the stock is affected by market demand and the catch rate,and the dynamic equations of the catch rate and the unit price of the stock are added to the model.For this model,we consider the effects of time delays,stage structure and Allee effect on population growth,and consider the dynamic properties of the systems,that is,the local stability and bifurcation near the equilibrium,as well as the optimal control problem and H∞ control problem.The main work is as follows:1.A fishery economic model with two time delays is established.The influence of time delays on the local stability around the internal equilibrium and the conditions for stability and Hopf bifurcation are considered.Secondly,the direction of Hopf bifurcation and the stability of bifurcation periodic solution are analyzed.Then the optimal cost control is designed to achieve the maximum net profit and the minimum the waste caused by hoarding for speculation,it also maintain the stability of the system.The guidance intervention control with time delays and minimum the waste caused by hoarding for speculation is also designed.Finally,the validity of the theoretical results is verified by numerical simulation.2.A delayed fishery economic model with stage structure and Allee effect is established.The effects of catch and economic factors on population extinction or persistence are considered.The influence of time delay on the dynamic properties of the system is obtained.The system is locally stable around the interior equilibrium when the parameters are in a specific range,and the Hopf bifurcation can occur as the time delays cross the critical values:Then we invest the direction of Hopf bifurcation and the stability of bifurcated periodic solutions.In addition,the T-S fuzzy model of the system is constructed,and the H∞ fuzzy controller is designed to eliminate the bifurcation phenomenon by using a linear matrix inequality approach.Finally,the validity of the theoretical results is verified by numerical simulation.