Design And Application Of Chaotic Circuits Containing Charge-controlled Memristors And Magnet-controlled Memristor

Memristor is widely used in the realization of circuits and systems such as chaos,memory and neural network due to its characteristics of memory and nonlinearity.However,the literature research in recent years shows that a lot of research results tend to study the memristor itself,but there are relatively few researches on the memristor chaotic system.Therefore,in order to solve this problem,this paper establishes and expands the types of memristor chaotic system by combining the memristor with Lüchaotic system.With the continuous development of chaos control theory,chaos control has become one of the hot spots in nonlinear science research.Therefore,using the control methods in modern control theory to control chaotic systems can provide reference value for solving the problems that various systems are troubled by chaotic phenomena in real life.Among them,alternate control is a simple and low cost control method,and can simplify the complexity of the system.It is very important to apply alternate control method to chaos control and synchronization research.In this paper,a five-dimensional memristor chaotic circuit is designed by using a magnetically controlled memristor and a charge-controlled memristor.To draw a scientific conclusion,this paper regards memristor chaotic system as the research object.Finally,the system is applied to speech encryption.The main research work is as follows:(1)On the basis of three-dimensional chaotic system,the mathematical models of two kinds of memristors are added as feedback items to design a new five-dimensional memristor chaotic system model.The memristor chaotic system is taken as the research object of this paper.According to the method of characterizing chaotic motion,the dynamic characteristics of the system are studied from the perspective of phase orbit diagram,power spectrum,Lyapunov exponent spectrum and bifurcation diagram.The influence of different parameters on the dynamic behavior of the system is sufficient analyzed.The results of it show that the designed memristor chaotic system will not only exhibit chaotic phenomena within the appropriate parameter range,but also exhibit rich chaotic behaviors with the change of parameters.A new mathematical model of memristor chaotic system is proposed,which provides a new idea and scheme for the modeling of memristor circuit system.(2)The designed memristor chaotic system is applied to chaos control under alternate control.The stability control of the system is realized by means of numerical derivation and simulation verification using the alternate control method.Then the controller with time delay and the controller based on event triggering are designed.The chaos control problem of the new chaotic system is studied by numerical simulation analysis,and the effectiveness of the designed controller is verified.It provides some new ideas and ideas for chaos control theory to control the designed memristor chaotic system by using alternate control and the extended alternate control method.(3)Taking the newly constructed five-dimensional memristor chaotic system as an example.Firstly,the master-slave system is reconstructed by adding state observers to the master-slave system respectively,and the master-slave system is synchronized under the action of the controller.The effectiveness of this method is verified by numerical simulation experiments;Secondly,the synchronization method is used to design a secure communication scheme.Lastly,through this scheme and simulation verification,the application of the designed memristor chaotic system in secure communication is realized.Through theoretical proof and numerical simulation,the designed memristor chaotic circuit can be applied in practice,which provides a new reference value for chaotic secure communication schemes and has a very broad prospect.