Stability Analysis Of Multimode Oscillations In The Coupled Memristor Oscillatory Circuit

The memristor is a new electronic component,with basic physical properties similar to the resistor.While it also have its own unique properties different from the resistor.It is a memory function of nonlinear resistor and can remember the number of charges flowing through memristor.In other words,by measuring the resistance change of the memristor,we can calculate the amount of charges flowing through memristor.Meanwhile,this change can be maintained when the power supply is cut off,which is one of the reasons for the memristor as a natural nonvolatile memory.With the rapid development of modern society,the advent of the information age,the demand for mass data storage and processing is very urgent.Because of its higher storage density,faster access time and low-power consumption,the memristor has the characteristics of nonvolatile memory.It can record the information in a very short time in the form of resistance transients.The whole process takes only a few joules of energy.If we download the data to the memristor,the data will not be lost even if the power supply is cut off.As long as the energizing power,the former state of resistance can be restored,so that "memory" before loading the data.This provide new innovative idea and solution to the field of circuit design,processing and storage of big data.At the same time,the memristor has the advantages of nonvolatile storage,high integration,strong memory,fast access time and low energy consumption.In circuit design,with the addition of the memristor,the integrated circuit can be more miniature on the basis of the existing components,and the running speed of the computation is faster,and the power consumption is lower.The memristor circuit is applied to artificial intelligence(AI),to reduce the scale of artificial intelligence(AI).At the same time,it can also enhance the ability of intelligent information processing.In the processing and storage of big data,the advantage of memristor is more obvious than that of traditional storage media,which will greatly improve the current storage architecture and methods,and the addition of memristor is an excellent solution to store and process large data.The memristor is introduced into the nonlinear circuit by using the nonlinear characteristic of the memristor and the nanometer size,and can generate the oscillation signal and produce some chaotic dynamical behaviors,which provides a new idea for the study of nonlinear circuits.At the same time,the study of the stability,chaos,bifurcation and other dynamic behavior of the oscillation circuit based on memristor has attracted more and more attention in reality.It is very important to study the stability condition of the oscillation circuit,which can be used to guide the practical application.Meanwhile,the coupled memristor oscillation circuit also has the function of filtering,energy storage,energy transmission and isolation impedance transformation.However,at present,most of the coupled oscillation systems are limited to the coupling of two oscillators.But,in practical applications,the system of mutual synchronization contains a large number of oscillators.Therefore,it is very important to analyze the stability of multi-mode oscillations in multi-coupled oscillation system.It is very important to design the multi-coupled oscillation system and analyze the stability of the multi-mode oscillation,based on the research of the characteristics of memristor and the stability analysis of multi-mode oscillation of multi-coupled oscillation system.Therefore,we design the oscillator circuit based on memristor in the second chapter of this thesis.The multi-coupled oscillation system is established by memristor oscillation circuit with inductor.Without loss of generality,three coupled oscillator circuits are mainly discussed.We use the equivalent linearization technique of Krylov–Bogoliubov and the Jacobian matrix of systems to analyze the stability of multimode oscillation of such circuits,and the numerical simulation and analysis are carried out,these simulations verified the correctness of our theoretical analyses.Finally,we also designed the circuit to couple the oscillator circuit with capacitance,and made a simple circuit analysis.Then,we take this opportunity to describe our next job prospects,and the conclusions of this thesis are summarized.