離心調速器之渾沌同步與反控制

Abstract

本篇論文研究離心調速器非線性系統的渾沌同步與反控制 . 藉由產生一個相同於原系統的方程式 , 利用不同的耦合項去使兩相同系統但初始值不同的渾沌系統同步 , 最後以李亞普諾夫指數以及系統同步時間去驗證臨界強度值 . 接著引進歐幾里得幾何距離去做單向暫態時間的系統同步 , 並作出一耦合強度與距離的關係圖 . 最後以原渾沌系統為載波並加上正弦訊號去模擬秘密通訊 , 模擬結果證實加密訊號能完整解碼達成秘密通訊的要求 . 第二部分是以外加控制項去使原本有週期解改變為渾沌行為以達成反控制的要求 . 並以外加頻率, 耦合強度與所產生的分叉圖的渾沌區域的範圍的長度作一三維的關係圖 , 進一步去了解三者之間的關係

Chaos synchronization and anticontrol of a centrifugal governor are studied in this thesis. By generating two identical systems, different coupling terms are used to synchronize the chaotic systems with different initial conditions. And Lyapunov exponent and synchronous time are used to confirm the critical coupling strength. Then Euclidean distance is used to make unidirectional synchronization and plot a figure with coupling strength vs the distance. Finally the secret communication is simulated. Chaotic systems are used to a sinusoidal carry signals. The results shows that encoded signals can completely decode and satisfy the demand for secret communication.