Two Kinds Of State Feedback Impulsive Models And Dynamic Analysis In Freshwater Aquaculture And Commodity Price Regulation

In recent years,the theory of state feedback impulsive differential equation has been gradually improved,and it has been widely used in the fields of biological population protection,infectious disease prevention,computer virus control and so on,and solved some practical problems.In this paper,the problems of phytoplankton control in pond culture and commodity price fluctuation in market economy are considered,and two kinds of state feedback impulsive models are put forward.By analyzing the dynamic properties of the models,the conditions for phytoplankton and cultured fish to achieve ecological balance and maintain commodity price stability are obtained.In Chapter 1,the phenomenon of water bloom caused by excessive phytoplankton in pond culture and the price fluctuation of market commodities are expounded,and the state feedback impulsive control measures are considered as research methods for regulation.In Chapter 2,some preliminary knowledge about semi-continuous dynamical systems are introduced,which provides theoretical support for the following research work.In Chapter 3,the global dynamics of the state feedback impulsive model for maintaining the ecological balance of pond culture is introduced.Firstly,a mathematical model reflecting the predation relationship between phytoplankton and cultured fish in ponds is established,and on this basis,state-dependent unilateral impulsive control measures and bilateral impulsive control measures are considered as adjustment strategies.Then,the global dynamics of the model is analyzed by using the relevant theoretical knowledge of ordinary differential equations and semi-continuous dynamical systems,and the existence conditions of unilateral control order-1 periodic solution and bilateral control order-1 periodic solution of the state feedback impulsive model are found respectively,and the asymptotic stability of its orbit is verified.Finally,the most effective way to prevent water bloom,maintain fish cultivation and the stable circulation of pond ecology is explored.In Chapter 4,the global dynamics of the state feedback impulsive model to maintain the relative stability of commodity prices is introduced.Firstly,the relationship between commodity price and output is explored.On this basis,we try to add state-dependent bilateral impulsive control measures as price adjustment strategies,and further analyze the improved model under policy intervention and the unilateral state feedback impulsive control model under the situation of market demand exceeding supply.Then,the global dynamics analysis of these models is carried out,and the existence of unilateral control order-1 periodic solution and bilateral control order-1 periodic solution and their orbital asymptotic stability are discussed.Finally,further explored the effectiveness of price control.The chapter 5 mainly summarized this paper and looks forward to the future work.