Stability Analysis And Control Of Economic System With Delay And Impulse

Economy decides the development of a country. The stability problem of economical systems as an actual problem is attracting more and more attention. We need to pay more attention to the stability problem of economic systems, especially when the economic crisis has happened and many governments rescued the market. How to control the unstable economic systems to make the systems develop under healthy direction is a significant research with actual meaning. In this paper, price system and advertisement model are studied. The stability problem of economic systems with delay and impulse is studied by way of the comparison theorem of differential equations and Lyapunov function. Some sufficient conditions for the asymptotic stability of the system are obtained, so provide a new method and concept on resolving related problems.The main content is depicted as follows: In the first chapter, the research background and meaning, current research situation and research content and concept of the control of price system are introduced and summarized. In the second chapter, some concepts and theories are introduced. In the third chapter, the impulsive control problem of a price system is studied. Some sufficient conditions for the asymptotical stability of the system are obtained by comparison theorem of impulsive differential equations, and the upper bound of impulsive intervals is estimated. The system can be stable as long as possible, and avoid inflation or deflation phenomenon happen. The result illustrated to be efficient through the emulation carried on with Matlab. In the fourth chapter, the stable problem of a price system with time-delayed and impulse is discussed. A sufficient condition of asymptotical stability of its zero solution under time-delay impulsive control is derived, and the condition reflects the relationship between the system parameters, impulse intervals and time delays. The result finally illustrated to be efficient through the emulation carried on with Matlab. The paper also presents economics explanation. In the fifth chapter, the stable problem of a economic model with advertising time-delayed and impulsive is discussed. By the stability theorem of differential equations and Lyapunov functions, a sufficient condition of asymptotical stability of its zero solution under time-delay impulsive control is derived, and the condition reflects the relationship between the system parameters, impulse intervals and time delays. Theoretic analysis and numerical simulation show efficiency and feasibility of advertising time-delayed and impulsive control. It shows wide applying prospect of time delay and impulsive control in economic systems.