Complex Characteristics Analysis And Synchronization Control Research Of Chaotic Circuits With Single/dual Memristors

The memristor is a kind of nonlinear element,which can remember the amount of charge through it.Memristance of the memristor is changed by controlling the change of current.Besides,memristor also has good scalability,high integration density,low energy consumption,simple physical structure and so on,which makes it have great potential value and research significance in theoretical research and engineering application.Simultaneously,memristor becomes the fourth basic components after resistance,capacitance and inductance,which provides a new development space for circuit design and application of memristive circuit.In the thesis,the nonlinear dynamic behavior of the two memristor-based chaotic systems is discussed and the synchronization control between two memristor-based chaotic systems is studied.Then,color image is encrypted by the memristive chaotic sequence,and digital circuits of the memristor-based chaotic systems are designed.The main study work is summarized as follows:(1)Two kinds of memristor chaotic circuits with different topologies are built and the corresponding nonlinear dynamic behavior is analyzed.Firstly,for the single memristor-based chaotic system,the coexisting dynamics depending on system parameter and multistable behavior affected by initial values are analyzed.In particular,special bifurcation modes and the coexisting strange attractors are displayed.Secondly,the coexisting bifurcation modes of the systems with series-parallel memristors depending on system parameter are shown.The influence of the serial-parallel memristors on the chaotic oscillation and multistable characteristics of the system is analyzed.Finally,flux-chage model of the dual-memristor-based system is established to analyze the coexistence characteristics depending on system parameter,sensibility of the system to initial values and multi stability.(2)Nonlinear adaptive controllers are designed to realize generalized synchronization between heterogeneous memristive systems and image encryption is completed.First of all,an adaptive generalized synchronization method is proposed to design a nonlinear adaptive controller and update law of unknown parameters.The generalized synchronization between single-memristor and dual-memristor chaotic system is realized.Next,considering the influence of external disturbances,an adaptive sliding mode controller is designed to complete the adaptive generalized synchronization of the dual-memristor chaotic system and the single-memristor chaotic system with single-frequency disturbances.At last,a chaotic encryption scheme for color image is presented and the encryption of color image is completed by combining the multistbility characteristics of memristor-based system.Moreover,performance analysis of the proposed encryption algorithm is accomplished.(3)A scheme of memristor-based circuit based on FPGA technology is proposed,and the hardware design and circuit experiment are completed.To begin with,the system equations are discretized by using the fourth-order Runge-Kutta algorithm and the equation coefficients are converted into IEEE-754 floating-point numbers.Then,the three basic modules containing floating-point multiplier,floating-point adder,floating-point/fixed-point converter are introduced.Lastly,based on the FPGA technology,a scheme of designing memristor-based digital circuits is proposed and Verilog language is used to describe the circuit module.The program is compiled and downloaded to the FPGA board,and the corresponding hardware experiments are completed.