Research On Dynamic Behaviors Of Memristor Circuit With Lossless Transmission Line

Memristor is a kind of nonlinear circuit element with memory characteristics,which is suitable for introducing it into all kinds of classical circuits to construct all kinds of nonlinear memristor circuits.Memristor circuits have rich nonlinear dynamic behaviors and are widely used in many fields such as neural networks,secure communication and storage computing.The lossless transmission line is a basic circuit element that can carry electrical signals from one place to another and prevent energy loss during transmission.Therefore,nonlinear circuits based on lossless transmission lines are widely used in many fields,such as wireless sensor networks,new energy vehicles and so on.However,there are few studies on the dynamic behavior of memristor circuits based on lossless transmission lines.To solve this problem,this thesis will study the dynamic behaviors of memristor-based circuit with lossless transmission line.The main contents are as follows:(1)A memristor circuit system with lossless transmission lines is proposed,where the memristor is flux-controlled.Using Kirchhoff’s Current Law and Kirchhoff’s Voltage Law,the memristor circuit equation is simplified to a second-order neutral differential equation with time delay,and the conditions for global stability,local stability and Hopf bifurcation of the system are established.It is shown that the memristor parameters have a significant impact on the global stability and Hopf bifurcation of the system.Finally,two numerical examples are used to verify the validity and correctness of the theoretical analysis.(2)By choosing the length of the lossless transmission line and the memristor parameters as the chaotic control parameters,the chaotic phenomena of the circuit proposed in(1)are investigated.Based on Lyapunov exponent spectrum and bifurcation diagram,the condition of circuit chaos is obtained.Through simulation analysis,it is found that the circuit can generate two modes of chaotic attractors under different conditions: single scroll chaotic attractor and double scroll chaotic attractor.The sensitivity of chaos to initial conditions is investigated by choosing different initial conditions.Finally,the chaotic map generated by the designed circuit is applied to secure communication.The simulation results show that the chaotic map has better performance than other maps.