雙 Ge-Ku系統,Sprott 4系統及 Rossler系統的渾沌與渾沌同步

Abstract

本篇論文以相圖、龐卡萊映射圖、李亞普洛夫指數以及分歧圖等數值方法研究新Double Ge-Ku系統的渾沌現象。應用主動控制獲得雙重及多重渾沌交織同步。對此系統應用部分區域穩定性理論和實用漸進穩定理論來達成廣義同步。更進一步使用新模糊模型來研究Sprott 4 系統以及 Rossler 系統的模糊模型和渾沌同步。此外，將探討新模糊邏輯常數控制器應用在投影同步及含有不確定度的渾沌系統。在以上研究中，皆可由相圖和時間歷程圖得到驗證。

In this thesis, the chaotic behavior of new Double Ge-Ku system is studied by phase portraits, time histories, Poincaré maps, Lyapunov exponents and bifurcation diagrams. New type for chaotic synchronization, double and multiple symplectic synchronization, are obtained by active control. A new kind of chaotic generalized synchronization, different translation pragmatical generalized synchronization, is obtained by pragmatical asymptotical stability theorem and partial region stability theory. A new method, using new fuzzy model, is studied for fuzzy modeling and synchronization of Sprott 4 system and Rossler system. 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 are provided to verify the effectiveness of all above studies.