Research On Synchronization And Hybrid Synchronization Of Chaotic Financial System

Chaos exists widely in nonlinear systems.Its initial sensitivity and unpredictability are applied in many fields.In the nonlinear financial system,chaos will lead to a series of fluctuations in the financial system.If the financial system is not controlled,it is prone to financial crisis due to violent fluctuations.In the financial field,there will be a period of delay from the proposal to the implementation of a policy,which is an important reason for the widespread existence of time delay in chaotic financial system.The economic globalization,the economic development and information exchange of various regions and many other reasons lead to the mutual coupling between the various financial systems,and the mutual coupling between the two financial systems is inevitable.1.A class of time-delay chaotic financial system is constructed by adding time-delay term,and then the chaos characteristics of the system are presented and analyzed by Lyapunov exponential spectrum and bifurcation graph.Based on the theory of system stability,a simple adaptive linear synchronization controller is proposed to realize the synchronization of the system.For the coexistence of synchronization and anti synchronization,i.e.hybrid synchronization,the existence of hybrid synchronization problem for chaotic systems with time delay is determined by solving equations algorithm.Two delayed chaotic financial systems with different initial values are synchronized by adaptive synchronization controller.2.Based on the original bidirectional coupled chaotic system with the same dimension,by adding scale matrix,construct bidirectional coupled chaotic system with different dimensions.Then,using the direct design method,a synchronization controller is proposed to synchronize two bidirectional coupled chaotic systems with different dimensions in two different dimensions.3.The above theoretical results are simulated by MATLAB software.The simulation results verify the rationality and correctness of the proposed synchronization scheme,and prospect the future research direction.This thesis also introduces and generalizes the places that can be researched in the future.