Ge-Ku-van der Pol系統及Sprott 22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Ge-Ku-van der Pol系統的渾沌現象。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；應用主動控制獲得雙重及多重渾沌交織同步。更進一步使用新模糊模型來研究Sprott 22系統的模糊模型化和渾沌同步。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 in new Ge-Ku-van der Pol system is studied by phase portraits, time history, Poincaré 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 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.