Multi-stable Analysis And Chaotic Synchronization Control Of The Triple Active Memristive System

Memristor is a nonlinear two-terminal device with memory which is referred as the fourth basic circuit element in addition to resistance,capacitance,and inductance.It has been widely investigated in signal processing,artificial intelligence,chaotic circuit design and so on due to its lots of advantages,such as memory,non-volatility,highly integrated density,nanoscale structure,etc.The memristive chaotic system is very sensitive to initial values and its dynamic behaviors are more abundant and complicated,which makes it have potential application value and prospect in synchronization and secure communication.In this paper,two different memristive chaotic systems are first proposed with active cubic flux-controlled memristors.A series of analyses and comparative studies of these systems are carried out on multistability,synchronization and image encryption.The main work is listed as follows:(1)Two different memristive chaotic systems are proposed,and the analyses of multistability and circuit implementations are accomplished.At first,two four-dimensional memristive chaotic systems with different topologies are proposed based on the classical Lorenz system and Chua circuit,respectively.In addition,the system's stability is analyzed by the calculation of dissipative and equilibrium point set.The bifurcation diagrams,Lyapunov exponents,attractor basins and so on are carried out to investigate dynamic behaviors,especially multistability.At last,the equivalent circuits are designed by Multisim to complete the circuit simulation,and the experimental results verify the validity of these designs.(2)Two different synchronization controllers are designed to get the synchronization of memristive chaotic systems with same or different structure,respectively.Firstly,a controller for synchronization of same memristive chaotic systems is designed based on the open-loop-closed-loop control method to achieve synchronizations of proportional projection and functional projection.Secondly,the controller feedback function is changed to realize the switching tracking control of memristive chaotic systems.Finally,a nonlinear synchronization controller with exponential term is devised according to the differential equations of two different systems to realize the synchronization of different systems,and the multistability is considered in synchronization research.(3)The image encryption and comparison based on multistability are achieved,and the application of heterogeneous system synchronization in image encryption is completed.In the first place,the application of multi-stable coexistence phenomenon based on memristive chaotic systems in gray image encryption is realized,and the effects on image encryption of different stable states or different systems are compared and summarized.The multistability of memristive chaotic system is instructive for the choice of secret keys.What's more,the application of heterogeneous memristive chaotic systems in color image encryption is obtained by selecting the proper driving system and secret keys.The results indicate that the memristive chaotic system applied to image encryption has high research values and engineering significance.