Research On Stability And Synchronization Of Chaotic Financial Systems

Chaos is a unique phenomenon in nonlinear systems.It has the characteristics of randomness,boundedness,unpredictability and sensitivity.And simultaneously,it can be expressed by several differential equations.Therefore,chaos can be used to analyze complex and regular phenomena,which can be applied to various fields.Chaotic control of nonlinear economics and nonlinear finance has attracted more and more attention.The theory methods of stability of chaotic system,especially integer chaotic system,increasingly tend to improve.Now the researches focus on control and synchronization,that is how to construct a controller which is simple and linear even,while the fractionalorder chaotic system has been developed for more than 20 years,and it is more suitable for studying financial markets which are high variable and mobility.First of all,the synchronization control of chaotic systems has synchronization and anti-synchronization.This thesis gradually discusses chaotic control,chaotic synchronization,and coexistence of synchronization and anti-synchronization of a class of fractional-order chaotic financial systems.For the stability of fractional-order chaotic financial systems,this thesis generalizes the stability theorem of integer order.Then,this thesis proposes a simple linear controller to achieve the purpose of control system stability.For synchronization of chaotic financial systems,this thesis uses adaptive control theory to achieve the purpose of synchronization.And for coexistence of synchronization and antisynchronization,that is,hybrid synchronization,this thesis uses the system stability theory to propose the conditions for hybrid synchronization of two fractional-order chaotic financial systems under arbitrary initial values,and the theory can be used to construct appropriate scores.A synchronous controller that implements hybrid synchronization.Secondly,considering that the state variables in the chaotic financial system will change with time,this thesis builds the chaotic financial system with time delay,and then uses the Lyapunov stability theory to get the conditions of asymptotic stability of the chaotic financial system.Thus we can get the controllers of chaotic system with time delay,and realize chaotic control of chaotic financial system with time delay.Simultaneously,based on the adaptive control theory,get the conditions for synchronization of two chaotic financial systems,and then design the controller to realize the chaotic synchronization of the two chaotic financial system with time delay.Finally,the numerical simulations of the above theoretical results are executed by Matlab software,which verify the rationality and accuracy of the results,and summaries and future research of financial system model has been proposed.