Stability Analysis And Control Of Some Complex Financial Systems

The stability problem of financial systems as an actual problem is attracting more and more attention.We need to pay more attention to the control problem of chaotic finance systems,especially when the American financial crisis is becoming more and more serious and many governments rescuing the markets.How to put controls on the chaotic economic systems to make the systems develop under healthy direction is a significant research with important actual meaning.This thesis mainly focuses on impulsive control,impulsive synchronization and time-delayed impulsive control of financial systems.And combine together with effective economic system,giving a very valid method to control the chaotic finance system.Chaotic theory is applied in economic systems,which provides a new method and concept on resolving financial crisis and it's related.The main content is depicted as follows:In the first chapter,research background and meaning,current research situation and research content and concept of the control of complex financial systems especially chaotic finance system are introduced and summarized.In the second chapter,some conceptions and theories are introduced. In the third chapter,impulsive control method of a kind of chaotic finance system is studied.Sufficient condition is derived with impulsive control at discrete moments, under which the unstable equilibrium point of the chaotic finance systems can be stabilized,and great upper bound of impulsive intervals can be obtained.Theoretic analysis and numerical simulation show efficiency and feasibility of impulsive control. Further more,we studied the influence of time-delay in impulsive control,and put forward time-delayed impulsive control method of a kind of chaotic finance system. The results show that the chaotic behavior of chaotic finance systems can be eliminated under time-delayed impulsive control,but there needs more rigid impulsive intervals,that is,more strong control condition.In the fourth chapter, impulsive synchronization of a kind of chaotic finance system is introduced.Theoretic analysis and numerical simulation show efficiency and feasibility of impulsive synchronization,and the chaotic finance systems with different initial values can achieve synchronized development.In the fifth chapter,stability analysis of an advertising impulsive model is studied.A theorem on the stability of impulsive control system is presented by advertising control at discrete moments.Through improved sufficient condition,the unstable equilibrium point of the advertising strategy can reach global exponential stability and global asymptotical stability,and great upper bound of impulsive intervals can be obtained.Theoretic analysis and numerical simulation show efficiency and feasibility of advertising control at discrete moments,which shows wide applying prospect of impulsive control in economic systems.