Study Of Dynamics And Synchronization Approaches Of The Fractional-order Memristive Chaotic Systems

Memristor is the fourth basic element proposed based on the completeness of the relationship between circuit variables.it has broad application prospects in fields such as data storage,biological neural system simulation and other fields.The fractional-order chaotic system is a complex form of movement unique to the nonlinear dynamic system,and it is a complex phenomenon widely existing in nature.Chaos synchronization is a common method in the field of image encryption and secure communication.Applying the chaotic masking can realize the secure transmission of data.In order to better promote the theoretical research of memristors,this thesis is based on the fractional-order differential,and it adopts a new type of memristor model,and structures the Chua's chaotic circuit to construct the research object of this thesis—fractional-order chaotic systems based on the memristor model.The main content of this paper is as follows:(1)Using Lyapunov stability theory and bifurcation theory,the dynamic characteristics of the system are analyzed in depth,including the stability of the system's equilibrium point,phase diagram,Lyapunov exponent with parameters and bifurcation diagrams.Through comparative analysis,it can be found that the fractional-order memristive chaotic system has rich dynamic characteristics,and the system parameters and initial conditions have a great influence on the chaotic system.(2)In this thesis,based on the analysis of dynamic characteristics of fractional-order memristive chaotic system,a new and practical ? projection synchronization method is proposed.The validity of the method is proved theoretically by using the Mittag-Leffler function and other mathematical tools.The case of chaos synchronization in image encryption and secure communication verifies the correctness of the theoretical analysis.