Abstract
In this thesis, the chaotic behavior in new Ge-Ku-Mathieu system is studied by phase portraits, time history, Poincare maps, Lyapunov exponent and bifurcation diagrams. A new kind of chaotic generalized synchronization, different translation pragmatical generalized synchronization, is obtained by pragmatical asymptotical stability theorem and partial region stability theory. Second new type for chaotic synchronization, double and multiple symplectic synchronization, are obtained by active control. A new method, using new fuzzy model, is studied for fuzzy modeling and synchronization of Sprott 19, 22 systems. Moreover, the new fuzzy logic constant controller is studied for projective synchronization and chaotic system with uncertainty. Numerical analyses, such as phase portraits and time histories can be provided to verify the effectiveness in all above studies.
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