新Duffing-Van der Pol 系統的渾沌現象，實用渾沌廣義同步，辛同步，應用GYC部分區域穩定理論的渾沌同步及控制

Abstract

本篇論文以相圖、龐卡萊映射圖、Lyapunov 指數、分歧圖以及參數圖等數值方法研究新Duffing-Van der Pol 系統的渾沌現象。對此系統研究應用實用漸進穩定性理論和適應性控制法則來達成實用正反投影渾沌廣義同步；應用新動態表面控制和實用漸進穩定理論來獲得不同階系統之實用渾沌交織同步。更進一步使用GYC部分區域穩定理論來研究系統的廣義渾沌同步、渾沌控制和渾沌反控制。此外，將探討新Duffing-Van der Pol 系統以Legendre function為參數的渾沌行為及同步。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 Duffing-van der Pol system is studied by phase portraits, time history, Poincaré maps, Lyapunov exponent, bifurcation diagrams, and parametric diagram. A new kind of chaotic generalized synchronization system, pragmatical hybrid projective chaotic generalized synchronization (PHPCGS), is obtained by pragmatical asymptotical stability theorem and adaptive control law. Second new type for chaotic synchronization, pragmatical chaotic symplectic synchronization (PCSS), is obtained by new dynamic surface control and pragmatical asymptotical stability theorem. A new method, using GYC partial region stability theory, is studied for chaos synchronization, chaos control, and chaos anti-control. Moreover, the new Duffing-van der Pol system with Legendre function parameters is studied for chaos and synchronization. Numerical analyses, such as phase portraits and time histories can be provided to verify the effectiveness in all above studies.