Chaos Control And Chaos Synchronization In Typical Nonlinear Circuit System

There are a large number of nonlinear dynamical systems in many fields,such as mathematics,physics,biology,economics and engineering.Most of these systems have the characteristics of chaotic motion.The chaotic motion of the system may cause some uncertain effects in many aspects,such as the stability of the engineering work,the smooth operation of the electric power and the circuit network.Therefore,it is of theoretical significance and practical application value to study chaos control and chaos synchronization of nonlinear dynamical system.This paper discusses the existence of chaotic behavior in several typical nonlinear circuit systems by combining theoretical analysis with numerical simulation,and control the chaos by adjusting the system parameters.Moreover,an active controller is designed to generate chaos synchronization for two hyperchaotic systems.Some meaningful conclusions are obtained from the above research,which provides a different research method for the study of chaotic circuit systems.The main work of the full reserches including: Taking three typical circuit systems as the research object,the chaotic motion behavior in the system is discussed and studied respectively.For the variable capacitance diode circuit system,the two machine interconnected power system,Joseph Sen junction equivalent circuit system,First,the corresponding dynamic equation of the circuit system is obtained by using the principle of circuit,and then get the system non Dimensionalization,and then a two order nonlinear equation is obtained,and the solution of the equation is obtained by direct perturbation method.The analytic solution is a chaotic solution by the Melnikov chaos criterion theory,thus the chaotic behavior is turned out in the system.The correctness of the theoretical analysis is verified by numerical simulation results.By adjusting the parameters of the system in the Melnikov function,it is found that the chaotic behavior of the nonlinear circuit system can be effectively controlled.The chaotic synchronization of two hyperchaotic circuit systems is also studied in this paper.Based on the active control method,a nonlinear controller is designed to control and compensate the controlled system,so that the controlled hyperchaotic circuit system and the main system are synchronized,and the Lyapunov stability theory is used to prove that the error system between the two systems is stable,that is,the two systems reach the synchronous state.Finally,MATLAB is used to carry out numerical simulation,and the results also show that the scheme is effective.