帶回授控制的Lorenz系統的渾沌動力分析及其廣義同步

Abstract

本篇論文以相圖、頻譜分析、龐卡萊映射圖、分歧圖、李亞普諾夫指數、李亞普諾夫維度、平衡點分析、滑順控制與電路模擬等數值方法研究帶回授控制的勞倫茲系統的渾沌現象，並且以實際的電路麵包板與運算放大器等設備將此帶回授控制的勞倫茲系統實現於示波器上。對此系統應用部分區域穩定性理論來達成廣義同步。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 feedback control of Lorenz system is studied by phase portraits, power spectrum analysis, Poincaré maps, bifurcation diagrams, Lyapunov exponent, Lyapunov dimension, equilibrium analysis, sliding mode control and electronic circuit modeling, and we also realize the Lorenz system with feedback control on the oscilloscope by using electronic bread board, operational amplifier and other equipments. A new kind of chaotic generalized synchronization, is obtained by partial region stability theory. Numerical analyses, such as phase portraits and time histories can be provided to verify the effectiveness in all above studies.