Analysis And Application Of Extreme Multi-stable Characteristics Of Dual Memristive Shinriki Oscillator Circuit

Memristor is the fourth basic circuit component that describes the relationship between charge and flux.The resistance of memristor can be changed with the variation of current.So,the remristors are often referred to as generalized resistors with memory functions.Comparing with resistor,capacitor,and inductor,memristor has natural nonlinearity that allows them to construct chaotic circuits with very few components.In addition,the nano memristor has the characteristics of low power consumption,strong non-volatility and high integration density,and has a broad application prospect in memory devices,neural network,artificial intelligence and so on.In this thesis,two sets of memristive chaotic oscillation systems are constructed,and their dynamic behaviors are simulated separately in the voltage-current domain and the fluxcharge domain.Then,the hardware circuit experiments of the two sets of systems are completed,a color image encryption platform based on memristive chaotic sequences is designed.The main research contents are summarized as follows:(1)A Shinriki oscillator circuit with a quadratic flux-controlled memristor and a cubic charge-controlled memristor is proposed and the corresponding nonlinear characteristics are analyzed in the voltage-current domain.Firstly,a fifth-order mathematical model of the system is established,and the dissipation coefficient and equilibrium point set of the oscillator are calculated.Basic dynamic behaviors of the oscillator under different circuit parameters are analyzed,including coexisting bifurcations of different types,routes to period-chaos transitions,etc.Secondly,the phenomenon of antimonotonicity and multiple coexisting asymmetric attractors caused by the memristive parameters and the memristive initial values are demonstrated repectively with the help of Lyapunov exponents,bifurcation diagrams,and kinetic maps,etc.Finally,the extreme multistability of the oscillator depending on different initial state spaces of dynamical elements is observed through the attractor basins.(2)A shinriki oscillator circuit with two flux-controlled memristors of different polarities is constructed and the corresponding extreme multistability is reconstitued in the flux-charge domain.First of all,a dimensionality reduction model is obtained with the incremental fluxcharge modeling method,the set of plane equilibrium points related to the initial conditions of the memristors is converted into the determined equilibrium points.Next,the nonlinear phenomenon of the oscillator that depends on the circuit parameters,before and after dimension reduction,is observed through the traditional quantitative analysis methods.At last,dynamic behaviors of the oscillator are accurately predicted by evaluating the position and stability of the equilibrium points of the flux-charge model.Moreover,on the basis of this,extreme multistability reconstitution of the memristive oscillation system is realized.(3)The circuit experiments of two memristive chaotic systems are completed and a color image encryption platform is designed.To begin with,the digital module circuit of the system is constructed with the help of Verilog language and FPGA development board,and the trajectory diagrams of the attractors with different types are captured by an oscilloscope to verify the accuracy of the numerical simulations.Secondly,a color image encryption platform based on oscillator multi-stable sequences is proposed,and the encryption performance of the platform is evaluated based on simulation parameters and encryption effect diagrams.Then,the equivalent circuit components of the two memristor oscillation model the flux-charge domain are converted,and the hardware circuit is simulated through Multisim.The physical control of the extreme multistability is realized by adjusting five DC voltage sources.Lastly,a color image encryption platform based on the multistable sequence is proposed,the encryption process of the platform is designed with the help of Python and FPGA,and the encryption performance of the platform is evaluated according to the simulation parameters and the encrypted graphs.