Synchronization Analysis For A Kind Of Modified Chaotic Finance Systems

Financial system is an open and complicated nonliear system consisting of many elements, far away from equilibrium points. In this kind of complicated nonliear system, chaotic state appearing with the change of different parameters is a common phenomenon, due to the unbalanced condition of the system. Hence, financial synchronization is a parctical issue that econormists will confront. In this paper, we give a concise description on synchronization of chaotic systems and get the following new results:(1)Firstly, put forward a kind of modified chaotic finance system based on a kind of chaotic finance system.Then put forward a globally exponentially synchronization method for the kind of modified chaotic finance system with partial state variables as transmission signal. This method is combined with stability theory of differential equation theory, it turns the error system between driving-system and respone-system into two different parts, theory analysis shows the necessary condition of this globally exponentially synchronization method, numerical simulations show the effectiveness of this method. Then we put forward a synchronization method based on globally exponentially attractive set, pull in the definition of globally exponentially attractive set, applying this method to the kind of modified chaotic finance system and numerical simulations show the effectiveness of this method.(2)Based on Lyapunov stable theory and Routh-Hurwitz critrion theory, some effective controllers are designed for the global asymptotic synchronization on different conditions. This paper investigates the function projective synchronization of the kind of modified chaotic finance systems. When the system parameters are known, the hybrid feedback control and a method based on special matrix structure are adopted respectively to realize the synchronization of the chaotic finance system. When the system parameters are unknown, the active control is extended and introduced to realize the synchronization. Numerical simulations show the validity and the feasibility of the synchronization schemes. The results show that papers from a theoretical analysis of the feasibility of this approach, and then test by numerical simulation results show that this method is simple and design facilitate, results show the validity and the feasibility of the synchronization schemes.