應用GYC部分區域穩定理論於新 Froude-Duffing系統之廣義同步與控制，以Bessel 函數為參數的Rössler 系統之超渾沌，陰陽Rössler 系統的渾沌及實用混合投影廣義同步

Abstract

本篇論文以相圖、龐卡萊映射圖、Lyapunov 指數、分歧圖等數值方法研究新Froude-Duffing 系統的渾沌現象。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和渾沌控制。另外，將探討Rössler 系統以Bessel function為參數所激發出的超渾沌行為。最後，對於陰Rössler 系統的渾沌現象做歷史研究，並應用實用漸進穩定性理論和適應性控制法則來達成與陽Rössler 系統的混合投影渾沌廣義同步。

In this thesis, the chaotic behavior in a new Froude-Duffing System is studied by phase portraits, time history, Poincaré maps, Lyapunov exponent and bifurcation diagrams. A new method, using GYC partial region stability theory, is studied for chaos synchronization and chaos control. Hyperchaos of a Rössler System with Bessel Function Parameters is studied. A new kind of chaotic generalized synchronization system, hybrid projective Yin-Yang generalized synchronization (HPYYGS), is obtained by pragmatical asymptotical stability theorem and adaptive control law. Numerical analyses, such as phase portraits and time histories can be provided to verify the effectiveness in all above studies.