Synchronization Approach On A Class Of Nonlinear Chaotic Circuits By Applying Field Coupling

Chaos is an interesting phenomenon in nature,and it has rich dynamic behavior,such as high sensitivity,instability and unpredictability with the initial conditions.Therefore,chaotic systems have attracted more and more attentions in science and technology.The hyperchaotic system is developed from the chaotic system,and has more complex dynamic characteristics.A class of low dimensional chaotic circuits is discussed in this paper,and the chaos control and chaos synchronization are demonstrated.The outline of this paper is organized as follows.Firstly,the development of chaos,characteristics of chaos circuit,chaos control and chaos synchronization is briefly recalled.The differences between many control and synchronization strategy are analyzed.Some theories of chaos system and several main analysis methods for chaos systems are discussed in the second chapter.In the third chapter,based on a class of fourth-order chaotic circuit,the characteristics of the chaotic circuit are proposed.The equilibrium point in this chaotic circuit is stability controlled via linear feedback and single state variable.The feedback coefficients in control terms are obtained by Routh-Hurwitz criterion for given system parameters.The numerical results show that the proposed scheme is valid.In the fourth chapter,the synchronization of the fourth-order chaotic circuit is studied.The synchronization between two hyperchaotic systems,and the synchronization between two periodic systems,and the synchronization between hyperchaotic systems and periodic systems are discussed by voltage coupling,electric field coupling and magnetic field coupling,respectively.It is found that when the same systems are coupled,the complete synchronization can be achieved.If the different systems are coupled,the interference of capacitance and inductance in the coupling channel can effectively reduce the output difference between the two circuits,but the complete synchronization can not been achieved,and only intermittent synchronization be arrived.Furthermore,the distribution of average energy consumption of coupling channel is calculated in the space of two coupling intensities to find the dependence of average energy consumption on parameters of the system.Electric field coupling is triggered when two circuits are connected via a capacitor and the electric field energy is transmitted between the coupled circuits,which depends on the charge and discharge of the coupling capacitor.And magnetic field coupling is induced when two circuits are connected via an inductor and the magnetic field energy is transmitted between the coupled circuits by generating time-varying induced electromotive force,which can impose continuous feedback on each circuit.It is beneficial to energy exchange in coupling circuits to realize system synchronization by adjusting the parameters of coupling channel.Finally,the stability of the system synchronization is further verified by the circuit simulation software.The conclusion is given in the fifth chapter.