Research On Memristor-based Chaotic System With Application

Memristor theory was proposed as early as fifty years ago.Memristor is circuit element which used to describe the relationship between magnetic flux and charge.In 2008,the discovery of the HP memristor has a milestone significance,which has ignited the upsurge of domestic and foreign scholars' research on memristor.Since the memristor is still unable to get out of the laboratory at present,the realization of a simulator equivalent to the memristor characteristic through the current circuit technology has become an effective method on researching memristor.Since the memristor has a natural nonlinearity,it can constitute a chaotic circuit system with few components.Researching the chaotic behavior and mechanism and achieving the control laws of the memristive chaotic system can help us to understand the mechanism of the natural world.On the one hand,we can apply memristive chaos circuit to engineering application to benefit humanity.Therefore,it is of theoretical significance and application value to research the memristive chaotic system.The work of this paper is mainly divided into two parts,research on simulator of memristor and resarch on memristive chaotic systems.In the simulator of memristors,a floating type charge control memristor simulator based on AD844 current feedback operational amplifier was designed.It is different from the flux control memristor designed by most scholars,and it is a simulator closer to the real thing of HP memristor.Moreover,the floating design of the simulator memristor is realized,and the grounding restriction required for the general simulated memristor is eliminated.Multisim simulation results show that the simulator can well simulate the characteristics of the memristor.Further,the influence of the internal parameters of the simulator circuit on the characteristic of the simulator memristor is researched.In the memristive chaotic system,a chaotic circuit based on the quadratic memristor is presented.The mathematical model of the circuit is established and the dynamic characteristics of the model are analyzed.The positive Lyapunov exponent of the system shows that the circuit has chaotic phenomenon.The routes of period doubling bifurcation leads the system to chaos.Moreover,a synchronization method based on driving-response realization of memristive chaotic circuits is designed.The above conclusions are verified by Multisim simulation.Two synchronization control laws of memristive chaotic systems are designed.One is based on the state observer theory,which transforms the chaos synchronization problem into a state observation problem.One is memristive chaotic system finite-time synchronization control law.The finite-time synchronization problem of memristive chaotic systems is transformed into the finite-time stability problem of the error system.The Matlab numerical simulation results show that the two control laws achieve the synchronization of the memristive chaotic system.Finally,a state observer-based memristive chaotic secure communication system scheme is designed.Theoretical analysis and simulation results show that the proposed scheme can reduce the number of communication channels compared to the chaos masking scheme and effectively enhance the confidentiality of communication.