Synchronization Control Research For A Kind Of Finance Chaotic Systems

Financial system is of an open nonlinear system consisting of many elements, far away off equilibrium points. In this kind of complicated nonlinear system, chaotic state appearing with the change of different parameters is a common phemomenon, due to the unbalanced condition of the system; Furthermore, financial synchronization is also a practical issue that econormists will confront. For example, how to realize financial synchronization between the developed countries and that of between countries of the developed and the developing during the process of econormic globlization.Firstly, VFC equilibrium points control method is put forword in the paper, focusing on the resolution of this kind of financial chaotic system. Both theoretic analysis and numerical simulation show that the chaotic behavior of financial system can be eliminated. The unproper union of parameters in the system is the root resulting in chaotic state, which may make the system out of control or lock it ultimately. However, VFC equilibrium control method, can control the system to equilibrium points. It can not only change financial system from chaotic state into good order, but also eliminate arbitrage, and finacial risks are reduced thereafter.Secondly, based on Lyapunov stable theory, a kind of control method which can achieve the financial synchronization is designed to cope with the different condition of the financial chaotic system, by means of constructing proper control function. Both theoretic analysis and numerical simulation show that synchronization comes true theoretically not only in financial chaotic systems with different variables but also in systems with certain parameters and uncertain ones. Moreover, another kind of synchronization control method raises for two criteria of chaotic systems which share the same structures with different initial values. The method originates from the judgment based both on nature of row strictly diagonally dominant matrix and on the stable theory of differential equation.That is, if the matrix of the error system coming from driving chaotic systems and response chaotic systems is that of row strictly diagonally dominant, the two financial chaotic systems share synchronization definitely. Numerical simulation shows the effectivness of the method. The method has an obvious advantage of avoiding the troubles in dealing with the approximate disposal and constructing Lyaponov function to make a controller. The two methods mentioned above offer, to a certain extent, the theoretical guidance and principles to acheive financial synchronization and harmounious development in some regions and countries with unbalanced ecomonic development.Finally, a synchronization control method based on diagonally dominant criteria is compared with the method of nonlinear coupling synchronization. Numerical simulation shows that the former performs a stronger robust in synchronization. That is to say, finacial synchronization can be oprerated more efficiently by means of the synchronization control based on diagonally dominant criteria for the regions and countries with simliar or same econormic structures.