Study On Tri-valued Memristor Modelling And Its Application In Chaotic Circuits

Memristor is a passive nonlinear element with memory characteristics,and are the four basic circuit elements together with the resistor,the capacitor and the inductor.It has been nearly half a century since the first introduction of the memristor,and related researches have mainly focused on two aspects of binary and continuous memristors.However,compared with these two types of memristors,the tri-valued and multi-valued memristors are better than binary and continuous memristors because they can carry more information,have rich features and great research potential in logic circuit and chaotic circuit.Thence,it is worth to explore various models of tri-valued memristor,its circuit features and investigate its applications.Meanwhile,previous researches and applications show that the series-parallel connection on circuits of memristor creates more diverse circuit performances,more excellent capacities and more extensive applications.Prior researches mainly focus on theoretical investigation of series-parallel connection based on a mathematical perspective.But,researches on circuit simulation and experimental verification are relative scarce.For this reason,it is necessary to analyze and verify the properties of memristors series-parallel connection with experiments.Based on the review of preceding researches,this study will propose the notion of tri-valued memristor,study the mathematical model,Simulink model and Spice circuit model of tri-valued memristor,and its circuit behaviors are analyzed.Based on this,the analysis of the cascade characteristics of the tri-valued memristor and the application of tri-valued memristor to chaotic system are completed.The contents and innovations of this study are as follows:(1)The concept of tri-valued memristor is proposed for the first time,and a specific mathematical model of an ideal tri-valued memristor is given.A Simulink model and a LTspice software model are established,and its non-volatile,hysteresis characteristics of voltage and current under sinusoidal signal excitation,resistance,resistance state and hysteresis curve vary with parameters are analyzed.(2)The properties of series-parallel connection on circuit of memristor are discussed.The series and parallel equivalent rules of the extended memristor and tri-valued memristor are given theoretically.The influence of the parameters on the equivalent memristance of the tri-valued memristor after series and parallel connection is analyzed,and the conclusion is verified by simulation.(3)In order to investigate the application of tri-valued memristor in chaotic system,a hyperchaotic system with tri-valued memristor is constructed.The phase diagram,Lyapunov exponent,dissipation and other algorithms are used to analyze the characteristics of the system,andthe effect of system parameters on the dynamic characteristics of the hyperchaotic system has been studied.