Research On Hyperchaotic System Based On Memristor And Its Circuit Implementation

The memristor is the fourth basic circuit element following the resistors,capacitors,and inductors and is used to describe the relationship between the magnetic flux and the charge.As a nonlinear circuit element with memory characteristics,the application of memristor in chaotic circuits has become a hot topic.Compared with classical chaotic systems,chaotic systems introduced by memristors have more complex dynamic characteristics.Therefore,the design and hardware implementation of the chaotic circuit with memristor have more practical value.In memristor chaotic systems,most of them involve the memristor as the system's negative feedback,and a few literatures use the memristor as the positive feedback of the chaotic system.In this paper,based on the system construction mechanism of hyperchaotic memristor system,starting from the single parameter controlled Lorenz chaotic system,a smooth quadratic nonlinear model design of memristor is used to simulate and hardware realize memristor hyperchaotic circuits.The thesis first briefly describes the basic theory of memristor and three memristor models,introduces the mechanism of the hyperchaotic circuit of the memristor,and verifies the chaotic state of the system by computing the system's Lee's index,equilibrium point set,and stability.By calculating the properties of the chaotic system,such as the Lee's exponent spectrum,phase diagram,bifurcation diagram,and information entropy,the dynamic characteristics of the hyperchaotic system of memristor are analyzed.The dynamic characteristics of the classical Lorenz chaotic system and the single-parameter controlled Lorenz chaotic system are analyzed and compared to verify the complexity of the dynamical behavior of the hyperchaotic system of the memristor.In order to verify the consistency between the memristor numerical simulation and circuit realization results,this paper first simulates the classical Lorenz chaotic system,the single parameter controlled Lorenz chaotic system and the hyperchaotic memristor system through MATLAB software.The phase diagram and the bifurcation diagram The difference between the dynamic characteristics of three kinds of chaotic systems is analyzed and contrasted from the perspective of Lee's exponent spectrum and information entropy.In the stage of circuit realization,the memristor model of HP Labs was first used to realize the HP memristive resistance through Multisim simulation and hardware.The difference between the HP memristor model and the quadratic smooth nonlinear memristor model circuit is realized by constructing an instrument model.Then,a modified chaotic circuit design method is used to design a single parameter controlled Lorenz chaotic circuit,and based on the memory The mechanism of the hyperchaotic system of the resistor is designed and the memristor hyperchaotic circuit is designed.The hyperchaotic circuit of memristor is realized by Multisim simulation and hardware.The numerical simulation analysis of chaotic system is used to verify the numerical simulation of the chaotic system and the consistency of the circuit implementation.It lays the foundation for the engineering application of hyperchaotic memristor system.