Switching Synchronization Control For Non-autonomous Chaotic Systems

As an important branch of nonlinear science,chaos has been widely studied in biology,engineering,economics and communication.Because of its randomness,continuous wide spectrum and extreme sensitivity to initial value,chaotic system is especially suitable for secure communication and image encryption,and chaos synchronization control is the key link to realize chaos application.Scholars have found that chaotic switching synchronization based on the theory of discontinuous dynamic system has fast convergence characteristics and strong anti-interference ability,which has great potential value in engineering applications.In this thesis,the dynamic behavior of four nonlinear chaotic systems is analyzed.According to the theory of discontinuous dynamical systems,the analytical conditions of combination synchronization and switching projective synchronization are discussed.Through numerical simulation and analog circuit,two synchronization schemes are realized,which are novel and practical.The main study work is summarized as follows:(1)Classic nonautonomous chaotic systems are selected for dynamic behavior analysis and circuit implementation.Firstly,the system equations of two classical nonlinear systems Duffing and Van der Pol are reconstructed respectively to form two new research objects Van der Pol-Duffing and Memristor-Duffing system.Secondly,the dynamic behaviors and parameters tuning of the four chaotic systems are analyzed through the bifurcation diagram,Lyapunov exponent spectrum,phase diagram and attraction basin.Finally,the equivalent circuits of nonlinear systems are built based on Multisim software to verify the consistency of numerical simulation and circuit implementation.(2)Different synchronization schemes and control strategies are designed,and the analytical conditions of two kinds of synchronization are discussed.First of all,the research objects and parameter values of combination synchronization and switching projective synchronization are determined,and the corresponding control strategies are designed.Next,according to the theory of discontinuous dynamical systems,the boundaries,specific motion regions and motion laws of the controlled systems with feedback controllers are divided.At last,by calculating the corresponding G-function and its higher derivative,the specific analytical conditions for appearance and vanish of synchronization are analyzed.(3)The influence of control parameters on synchronization is studied,and the analog circuits of chaos synchronization are completed.To begin with,the numerical simulation is programmed and debugged according to the theoretical derivation process.Then,the influence of different control parameters on chaos synchronization is compared by parameter diagrams,and the combination synchronization and switching projective synchronization are realized based on appropriate control parameters.The synchronization track of system is described through time sequence diagram and phase diagram,and the synchronization effect of feedback controllers is observed.Lastly,according to the parameter values and system state equations,the analog circuits are designed and debugged to verify the correctness and feasibility of the control strategies.