Projective Synchronization Of Chaos Based On Differential Geometry Theory

Recent years, the differential geometry method is gradually used in the chaos control andsynchronization between chaos systems. However, the research about the differentialgeometry method is still in the initial state, the related literatures are less. In this paper, as aspecial subject study, the projective synchronization between chaos systems with thedifferential geometry method is discussed.In the first two chapters of the thesis, the definition and classification of chaossynchronization are introduced, as well as the basis of the differential geometry theory. Afterthat, the current research status for the chaos control problem is described, in which severalliteratures about chaos control problem are analyzed by the differential geometry method,such as chaos control via nonlinear feedback, MIMO decoupled feedback linearization andtime-delayed feedback of chaos control, etc.Based on the two previous chapters, chaos projective synchronization is studied by thedifferential geometry method. In the third chapter, projective synchronization between thedifferent structure chaos systems is discussed. According to the regular standard form of theerror system equations, the control strategy equations are deduced by the method of nonlinearfeedback linearization, thus projective synchronization between the chaos systems is achieved.Considering a new three-dimensional chaos system and a Chen-Lee chaos system as examples,numerical simulations are given to illustrate the effectiveness.In the fourth chapter, projection synchronization of the chain networks is investigatedbased on the theory of differential geometry theory. In accordance with the regular standardform of the error system equations, on the basis of the partial asymptotical stability methods,the functional control equations and zero dynamic equations are derived to achieve chaosprojective synchronization. Illustrated by NH3laser systems as the chain networks nodes,Matlab numerical simulations are shown to verify the synchronization principle.