Application Of Generalized Hamiltonian Systems To The Chaotic Synchronization

Based on the Generalized Hamiltonian systems' passivity observer designing methods, Sira-Ramirez and Cruz proposed the approach of the Generalized Hamiltonian systems and the observers dedicating to the chaotic synchronization in 2001.In this paper,the chaotic synchronization of several identical chaotic systems with or without time delay are considered by employing this approach.And the results of the chaotic synchronization are satisfying.At last,the numerical simulation is executed by employing the nonlinear dynamical software,WinPP.The results of the numerical simulation agree well to that of the theoretical analysis.It shows the validity of this approach.Supported by the National Natural Science Foundation of China under Grant NO.10702065, the synchronization of several identical chaotic systems is considered,and the results have important theoretical significance and potential value of application to private communication.This dissertation is organized as follows:Chapter 1 is the preparative knowledge,including some stability theories and the generalized Hamiltonian systems and the observer approach.In Chapter 2,employing the generalized Hamiltonian systems and the observer approach, the synchronization of several identical chaotic systems is studied,such as the L(u|¨) system,Van der Pol-Duffing system,Genesio system and SMIB power system,at last and the numerical simulation is executed by employing the software,WinPP.In Chapter 3,in the similar way,the synchronization of two identical time-delayed chaotic systems such as the Van der Pol-Duffing system and SMIB power system is studied, and also the correctness of the theoretical results is verified numerically.In Chapter 4,the conclusion is presented.