Dynamic Research And Circuit Realization Of Memristive Chaotic System

Since memristor was proposed,researchers at home and abroad have done extensive research on it.Memristor has the characteristics of memory,non-linearity and non-volatile.It provides a new scheme and idea for the study of nonlinear circuits and systems,neural networks,digital circuits and other fields,and is of great significance for the design of new memristor chaotic systems.Memristive chaotic systems can produce good pseudo-random chaotic signals,which can be used in image encryption,secure communication and other engineering fields.Therefore,it is of great significance and practical value to design memristive chaotic systems with more nonlinear phenomena and complex dynamic behaviors.In this context,this dissertation focuses on the design and circuit implementation of chaotic system based on memristor:(1)Based on the Sprott A system,a three-dimensional memristive chaotic system with no equilibrium point is designed.The system exhibits complex dynamical phenomena such as coexistence bifurcations,multi-stability,symmetric coexistence attractors and transient dynamics.Thus it is difficult to reproduce the accurate dynamics of the system,which is highly advantageous in encryption and communication.At the same time,an intermittent control scheme with adaptive mechanism is proposed to realize the complete synchronization of the memristive chaotic system.In addition,the circuit of the system is designed by modularization,the circuit is simulated by Mulitsim software,and the chaotic signal is generated by the system based on DSP(Digital Signal Processor)platform,which verifies the correctness of the numerical simulation of the system from many aspects.(2)Based on a three-dimensional jerk system,a four-dimensional memristive chaotic system with five-line equilibrium points is designed.Through numerical simulation and theoretical analysis,its rich and complex dynamic behaviors are studied.Specifically,transient dynamics of coexisting chaotic attractors with different amplitudes at different time scales are found.By selecting the appropriate parameters and initial conditions,the extreme multistability of mirror symmetric chaotic attractors,attractors with different amplitudes and periods can be observed.The study also found that,the initial condition of the memristor can be used as the controller to realize the offset boost of the attractors on the w-axis.Then,HSVII(Hybrid State Variable Incremental Integral)method is used to reduce the dimension of the system,and the relevant dynamics of the initial conditions of the system is transformed into the relevant dynamics of the system parameters,so as to realize the control of multi stability.Finally,the circuit implementation also proves that multi stability can be realized by voltage control.(3)Based on Hopfield neural network(HNN)model,a four-dimensional memristive hyperchaotic system is designed.Memristor is used to simulate the influence of electromagnetic induction on neurons in neural network.It is found that the parameters of the system have very good bifurcation structure,and the system has hyperchaotic phenomenon when different parameters and initial values are selected.At the same time,under special parameters and initial conditions,the system also has anti monotonicity.Finally,chaos attractors are generated based on Multisim platform and DSP platform.The experimental results are consistent with the numerical results of the system.