| Synchronization is one of the research hotspots in the field of nonlinear science and system control.The synchronization of chaotic systems has broad applications in many fields such as secure communication,biomedical engineering,medicine,financial systems,etc.This thesis investigates chaos synchronization of the master-slave generalized Lorenz systems via variable substitution control.The main works can be summarized as below.1.The synchronization scheme for the master-slave generalized Lorenz systems via variable substitution control is established,and chaos synchronization of the master-slave generalized Lorenz systems is transformed to a global stability or instability of a non-autonomous error system.2.Based on the theory of Lyapunov stability,some linear matrix inequality criteria for chaos synchronization of the master-slave generalized Lorenz systems via variable substitution control are proved,and some algebraic criteria for the master-slave generalized Lorenz systems to achieve global chaos synchronization or non synchronization via the various single-variable substitution control are obtained.3.Applying the obtained synchronization criteria of the master-slave generalized Lorenz systems to some famous chaotic systems,including the classical Lorenz systems,Chen systems,Lü systems,and unified chaotic systems,some algebraic criteria for global chaos synchronization or non synchronization of the master-slave synchronization schemes for these systems are established.The effectiveness of these criteria is numerically verified by examples.The obtained criteria for chaos synchronization and non synchronization of the masterslave generalized Lorenz systems can be expressed as the simple inequalities for the system parameters,which are easy to use in applications such as communication encryption. |
