| As an important part of the nonlinear field,chaos exists widely in natural science and social science.The application of chaos has attracted a large number of experts and scholars to study.With the gradual deepening of the research on chaos,chaotic system with richer and more complex dynamic behaviors are expected.Due to the nonlinear characteristics of the memristor,the dynamic characteristics of the chaotic circuit system based on the memristor element are more abundant than the general chaotic system.In the research of secure communication and image encryption,chaotic systems with more complex dynamic behaviors have higher practical value,so the research on synchronization control based on chaotic systems has been widely carried out.To avoid the loss caused by instability and further study by using chaotic behavior are the main research purposes of chaos control and chaos synchronization.In practical engineering,it is of far-reaching research significance to change the type of control according to the control demand and system state.Both intermittent control and impulsive control are the simple,low cost and effective control methods.Fuzzy control can simplify the complexity of system design and is especially suitable for the control of nonlinear and incomplete model systems.Therefore,a new Lorenz chaotic circuit based on memristive elements is designed to obtain signals with more complex dynamic characteristics,observe and analyze the dynamic characteristics,and then explore the selection the method of control to control the chaotic system.This research topic has practical needs and important significance.Through learning and research,this paper mainly achieved the following research results:(1)A memristive Lorenz chaotic circuit is designed based on a class of Lorenz chaotic system.The dynamic behavior of the system is analyzed,and a chaotic system with more complex dynamic behavior is obtained.Through the circuit simulation of the memristive Lorenz chaotic system,the SPICE simulation results are highly consistent with the numerical simulation results which proves the memristor characteristics and physical feasibility of the system.Firstly,the quadratic magnetron memristor is added to the basic Lorenz chaotic system to construct the memristive Lorenz chaotic circuit.Based on the dynamic analysis of the chaotic circuit system,the following conclusions are obtained : the system dissipation is less than zero,the asymptotic motion of the system tends to be an attractor,the Jacobian matrix of the system is solved to obtain that the system is unstable at the equilibrium point,the projection of the system ’s motion trajectory on the two-dimensional and three-dimensional planes has a double-turbine attractor and is consistent with the circuit simulation results,and the maximum Lyapunov index of the system is greater than zero,showing that the designed memristive chaotic system can produce more chaotic phenomena than the original chaotic system.The physical feasibility of the system is verified by the circuit diagram design of the simulation design.(2)For the Lorenz chaotic system,the method of pulse control combined with intermittent control is used to realize synchronous control.Compared with a single control method,the results of control are better to meet the control requirements and maintain the evolution state of the system.The method of the controller is to combine the control effect of alternating control and indirect control,improve the flexibility of the controller,so that the controller can automatically change the control intensity according to the different states of the system and the different control requirements.Based on Lyapunov stability theory,it is proved that the system realizes chaos synchronization under the proposed controller.Finally,a numerical example is used to verify that the designed controller can increase the positive or negative pulse at the time of the trigger condition in time to make the control effect of the system meet the expectation when the preset control intensity is enhanced or weakened,which leads to the change of the control.(3)For the Lorenz chaotic system,the fuzzy control method is used to realize the synchronous control.In the design of the controller,the response control method is added according to the added quadratic memristor.Compared with the original single fuzzy control,it has better control effect on the chaotic system with richer dynamic characteristics.The method of drive-response synchronization is adopted for the designed memristive chaotic system.On the one hand,the nonlinear part of the error system is approximated by the Mamdani fuzzy logic system.On the other hand,the controller is designed by the chaotic motion characteristics and the known nonlinear term generated by the quadratic memristor,and the stability of the error system under the controller is analyzed.By proving that the system reaches a stable state under the designed controller,the synchronous control of the memristive Lorenz chaotic system is realized,and the numerical simulation again verifies that the designed controller can design the controller under the condition that the nonlinear part is unknown.The controller is verified again by the tracking of the state variables of the drive-response system and the convergence of the error system. |
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