Research On Control And Synchronization Of Chaotic Financial System

Chaos is widespread in nonlinear financial systems.Many financial systems show extreme sensitivity and unpredictability to initial values.Therefore,how to realize the stability and controllability of the financial system is a problem worthy of in-depth study.At present,the research of integer order chaotic financial system has been gradually deepened,and the research of fractional chaotic financial system is still in the primary stage.The financial market is complex and changeable,and compared to the financial system of fractional order chaotic integer order chaotic financial system is more consistent with the actual financial market.For the time being,the fractional chaotic financial system still has many places worthy of deep research by scholars,such as mixed fractional order chaotic financial system synchronization control.Firstly,this paper aims at a new chaotic financial system model which is obtained by the proper coordinate dimension transformation of the classical chaotic financial system.The adaptive control method is used to design a single variable controller,which makes the chaotic financial system synchronize with the initial value of the chaotic financial system.In addition,a kind of algorithm to distinguish which variables can be used to realize anti-synchronization is given.It is applied to this kind of chaotic financial system and realizes the effect of the mixed synchronization of the chaotic financial system.In the same error system,when the controller is added differently,the final error system reaches a stable control time and the control effect is also different.Secondly,for a class of fractional financial systems,based on the adaptive control method,a simple single variable controller is designed to achieve the stability of the fractional order chaotic financial system.Then,using the linear feedback control method,the fractional order problem is converted into integer order,and the error system composed of fractional order chaotic financial system is composed of the fractional order chaotic financial system.The Lyapunov stability theory is used to obtain the sufficient conditions for the system to stabilize the error system and realize the mixed synchronization.In addition,through the hybrid synchronization criterion obtained,the effects of hybrid synchronization can be achieved in the case of a single controller and no external control,and the hybrid synchronization of the fractional-order financial system can also be achieved through this criterion.Finally,on the basis of the above theoretical analysis,this paper uses Matlab to simulate all the designed controllers,validates the effectiveness of the above methods,and looks forward to the future financial market and chaos research,and puts forward new research ideas.