帶回授控制的Liu-Chen系統的渾沌動力分析及其廣義同步

Abstract

本篇論文我們對Liu-Chen系統在第二項加入一個帶回授控制x4，並對其系統做相圖、龐卡萊映射圖、分歧圖、電路模擬、李亞普洛夫指數和穩定點的分析，分析其渾沌現象。對此系統應用ＧＹＣ部分區域穩定性理論來達成廣義同步和適應性同步，更應用滑順控制和模糊控制對其進行分析。在以上研究中，皆可由相圖和時間歷程圖得到驗證。

In this paper, we add a feedback control to Liu-Chen system and discuss the behaviors of the system by applying various techniques. These techniques include phase portraits, Poincaré maps, bifurcation diagrams, electronic circuit modeling, Lyapunov exponent diagrams and equilibrium analysis. The chaos synchronization uses GYC partial region stability of adaptive control, sliding mode control and fuzzy control. The chaos control uses fuzzy control. Numerical analyses, such as phase portraits and time histories can be provided to verify the effectiveness in all above studies.