Chaos Control And Synchronize Of Newton-Leipnik System And Complex Network

Historically,the study of synchronization Phenomena in dynamical Systems has been a subject of great interest since the earlier days of Physics,when Huygens found the locking between two weakly coupled pendulant in 17^th century Early studies on synchronizations were mainly related to frequency-or-Phase-lockings of Periodic motions.Recently the investigation of synchronization has been extended to chaotic Systems.Since 1990 Pecora and Carroll published synchronization in chaotic systems in Physics Review Letter,Chaos synchronization has become a significant topic. Many different forms of chaos synchronizations have been found,including complete synchronization,Phase synchronization,generalization synchronization, lag synchronization,Partial synchronization,and measure synchronization in Hamiltonian systems,and so on.In this Paper,we focus on the study of synchronization in coupled chaotic oscillators,and a number of interesting Phenomena were revealed.Approximate synchronization in the strong coupled systems and the chaos resynchronization in the strong coupled systems and the Patterns in the 2 dimensions coupled systems were discussed.In chapter 1,we briefly review the history and current progress on the studies of chaos synchronization.Complex networks and chaos synchronizations on the complex networks were also discussed.In chapter2,we introduce several commonly used methods of the chaos control: OGY methods,feedback control method,Backstepping control,adaptive control methods.In chapter 3,we firstly introduces the chaotic system Newton---Leipnik system which possesses two strange attractors.And then the backstepping design control approach is used to control Newton-Leipnik system to a steady state as well as tracking of a desire trajectory.The proposed controller is obtained by a systematic design approach and consists in recursive procedures that interlace the choice of a Lyapunov function according to the design of active control.Numerical simulations are provided to verify the feasibility and effectiveness.In chapter4 Effective adaptive controllers are proposed for stabilizing chaos to unstable equilibria.In addition,Chaos synchronization is achieved by employing active control scheme.Numerical simulations are provided to verify the feasibility and effectiveness,so the result of the control is mutually verified with the theoretical analyses and numerical simulations.In chapter5,the possibility and development of chaos synchronization in complex networks are introduced in brief.