四維度的Lü 系統的渾沌動力分析及其廣義同步

Abstract

本篇論文我們藉由在Lü 系統增加一個迴授控制器x4方程式來創造一個新的Lü 系統，並以相圖、時序圖、頻譜圖、龐卡萊映射圖、李亞普洛夫指數、李亞普洛夫維度以及分歧圖等數值方法來分析他的混沌現象。本論文將焦點擺在渾沌同步的數值模擬與電路模擬，同步理論包括自適性同步、GYC 部份穩定理論與BGYC 同步方法，而渾沌同步包括一般同步、廣義同步與變動參數廣義同步，最後比較數值模擬與電路模擬之一致性。在以上研究中，皆可由相圖和時間歷程圖得到驗證。

In thus thesis, we have presented a new Lü system by adding a feedback controller x4 equation of Lü system, and analyzed the chaotic behavior of new Lü system by phase portraits, time histories, Poincarѐ maps, Power Spectral, Lyapunov exponents, Lyapunov dimensions and bifurcation diagrams. This paper will focus on chaos synchronization of numerical simulation and circuit simulation. The chaos synchronization schemes are including originally adaptive synchronization, GYC partial region stability theory and BGYC synchronization. And the synchronization are including chaos synchronization, generalized synchronization and generalized synchronization of four dimensions Lü system with uncertain chaotic parameters. This thesis demonstrates three schemes of numerical simulation and circuit simulation, and then compares the consistency of two simulation results. Such as phase portraits and time histories can be provided to verify the effectiveness in all above studied.