| As a form of non-linear motion,chaotic synchronization exists widely in nature.Memristor has natural nonlinearity and can be used to construct chaotic systems to produce chaotic phenomena.The study of memristor and chaotic synchronization is helpful to better understand the laws of motion in nature and apply them to practice.In this paper,memristor and chaotic synchronization are studied.A memristor model is constructed and three different chaotic synchronization schemes are proposed by differential equation and cybernetics technology.The main contents are as follows:Aiming at the more complex model of partial memristor systems,a simplified memristor system is proposed.The system is simulated by Multisim and Matlab and input-output characteristics are analyzed in detail.In addition,two parallel circuits based on the memristor system,memristor and capacitor parallel circuit and memristor and inductor parallel circuit,are studied respectively.The influence of system variables is analyzed.These studies provide theoretical basis for our future applications in circuits.Aiming at the problem that some chaotic systems have fewer variables and the circuit is not easy to realize,a chaotic system is established and the dynamic behavior of the system is analyzed.The circuit diagrams are constructed by operational amplifiers,resistors,capacitors and multiplier.The numerical verification is carried out by Matlab and Multisim.A synchronization scheme,which is double-combination-compound synchronization with proportional matrix is proposed and studied.The corresponding controllers are designed by cybernetics technology and the double-combination-compound synchronization among multiple systems is realized.The simulation results show that the synchronization scheme has good correctness and reliability.Aiming at the problem of simple single path,external disturbance and system disorder in projection synchronization mode,a double combination projection synchronization for multi-chaotic systems is studied based on the projection synchronization and combination synchronization.Based on adaptive control law and Lyapunov stability theory,a sliding mode control surface and combination controllers are designed by non-singular sliding mode control technology.The double combination projection synchronization between two driving systems and multiple response systems is realized.In addition,some criteria and inferences of double combination projection synchronization are proposed.The effectiveness and flexibility of thesynchronization scheme are verified by numerical simulation.Aiming at the problem of information segment combination and easy loss of hierarchical transmission,multi-stage combination transmission synchronization is proposed.Based on Lyapunov stability theory,combination controller are designed by adaptive control technology,which realizes the transfer synchronization in stages after different systems are combined with each other.The feasibility and effectiveness of the synchronization scheme is proved by the numerical simulation.In this paper,the theory of non-linear system is explored in detail from the aspects of memristor system and chaos synchronization scheme.A simplest memristor system is constructed and three chaos synchronization schemes are proposed,which further expands the field of non-linear science and has certain scientific research significance and practical value. |
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