新Double-Froude系統的渾沌現象,應用GYC部分區域穩定理論的渾沌同步及控制，以Legendre函數為參數的Rössler系統之超渾沌現象與藉適應控制之Lü系統的陰陽廣義同步

Abstract

本論文由四個部份構成：(1)以相圖、龐卡萊映射圖、分岐圖及Lyapunov指數圖等數值方法研究新Double-Froude系統的渾沌行為。(2)應用部分區域穩定性理論研究廣義渾沌同步、渾沌控制。(3)探討Rössler系統以Legendre 函數為參數的超渾沌行為及同步(4) 藉實用漸進穩定理論為基礎的適應控制來探討陽Lü系統和陰Lü系統的陰陽廣義同步。

This thesis consists of four parts: (1) the chaotic behaviors of Double-Froude system are studied numerically by phase portraits, Pooincaré maps, bifurcation diagrams and Lyapunov exponent diagrams. (2) generalized synchronization and control of chaos is studied by GYC partial region stability theory. (3) the Rössler system with Legendre function is studied for chaos, hyperchaos and synchronization. (4) Yin-Yang generalized synchronization (YYGS) of Yang Lü and Yin Lü systems are studied by adaptive control based on pragmatical asymptotical stability theory.