新Mathieu-Duffing 系統的渾沌現象與其應用適應逆步控制及部分區域穩定理論之實用混合投影渾沌同步及辛渾沌同步

Abstract

本論文由三部分構成：（1）以相圖、龐卡萊映射圖、分岐圖、功率譜及Lyapunov指數圖等數值方法研究Mathieu – Duffing系統的渾沌行為。（2）用適應逆步控制在不同的初始條件下的兩個Mathieu – Duffing雙系統對不同的渾沌系統Duffing – van der Pol系統與 系統的實用混合投影渾沌同步及辛渾沌同步。（3）應用部分區域穩定性理論研究廣義渾沌同步、渾沌控制及實用混合投影渾沌同步。

This thesis consists of three parts: (1) the chaotic behaviors of are studied numerically by phase portraits, Poincaré maps, bifurcation diagrams, power spectrum and Lyapunov exponent diagrams. (2) system is studied for pragmatical hybrid projective hyperchaotic generalized synchronization (PHPHGS) and pragmatical hybrid projective and symplectic synchronization (PHPSS) with different kinds of different chaotic systems, Duffing-van der Pol system and system, by adaptive backstepping control. (3) chaotic generalized synchronization, chaos control and pragmatical hybrid projective generalized synchronization is studied by partial region stability theory.