臺灣博碩士論文加值系統

摘要
本論文主要探討兩混沌系統之同步化及其應用，所使用之動力系統為羅倫茲系統。首先探討羅倫茲系統之混沌行為，發現在多種不同參數組合之下，可以產生混沌行為；之後，選取可以產生混沌行為之參數，作為探討同步化及其安全通訊時所使用之混沌系統。本文所研究之同步化問題，兩系統之參數不同，起始狀況也不同，為區分起見，分別稱為驅動系統與反應系統。利用驅動系統訊號中某個變數驅動反應系統，給予反應系統的參數起始猜測值，擷取此驅動訊號與其在反應系統所對應訊號之時間序列，當作樣本，並令彼此之間的相關係數以及兩個訊號標準差之比值輪流趨近於1，當作收斂的指標，逐步修正參數值，直至收斂值在容頂~差範圍之內，如此則可達到同步化，使得兩個系統的參數值一樣。
接著應用同步化的觀念於安全通訊方面，在此為區分起見，分別稱兩系統為發射系統與接收系統，依上面所述之驅動變數，再加上一個欲傳遞之資訊訊號當作發射訊號，驅動接收系統，使用上述相同的收斂指標，逐步修正接收系統之參數，如此也可達到同步化，之後便可恢復此傳遞之資訊訊號。

Abstract
This thesis mainly focuses on the synchronization of two Chaotic systems, and its application. The Lorenz system is used as the dynamical system. First, the behaviors of the Lorenz system are explored. It’s discovered that the Lorenz system can have chaotic behaviors with many different combinations of parameters. Then, one combination of the parameters which causes the Lorenz system to be chaotic is selected as the chaotic system to be used in the synchronization and secure communication. The parameters and initial conditions of these two systems are different. In order to be distinguished, these two systems are described as the drive system and response system, respectively. One variable in the drive system is used to drive the response system. Given the initial guess of parameters in the response system, the time series of the drive signal and its counterpart in the response system are extracted as the samples. Making the correlation coefficient and the ratio of standard deviations between these two signals in turn approach asymptotically to one, which are the convergence criteria, the guessed values of the parameters can be adjusted gradually until the convergenced values are within the allowable tolerance. After the whole process is completed, the synchronization could be achieved, which means the parameters of two systems become the same.
The synchronization concept could be applied in the telecommunication security area. To be differentiated, two systems are named as transmitting system and receiving system separately. The transmitted signal to drive the receiving system includes the drive signal as mentioned above plus an information signal which needs to be transmitted. The same convergence criteria as mentioned above are also used to adjust the parameters of the receiving system progressively. In the same way, the synchronization could also be achieved so that the information could be recovered.

中文摘要Ⅰ
英文摘要Ⅱ
誌 謝Ⅳ
目 錄Ⅴ
圖目錄Ⅶ
表目錄Ⅹ
第一章、緒論1
1.1 研究背景與動機1
1.2 研究目的4
1.3 研究流程6
第二章、傅立葉理論7
2.1 傅立葉變換7
2.2 離散傅立葉變換8
2.3 快速傅立葉變換8
2.4 必v頻譜12
第三章、羅倫茲系統14
3.1 羅倫茲系統14
3.2 平衡點17
3.3 特徵值(Eigenvalue)17
3.3.1 平衡點(x=0,y=0,z=0)之特徵值18
3.3.2 平衡點(x= ,y= ,z= )之特徵值19
3.3.3 平衡點(x= ,y= ,z= )之特徵值20
3.4 羅倫茲系統之行為20
3.4.1 假設卅=10，γ=8/3，β變化20
3.4.2 假設卅=10，β=28，γ變化22
3.4.3 假設γ=8/3，β=28，卅變化23
第四章、混沌系統之同步化34
4-1 同步化之類型34
4-2 混沌系統同步化之另一方法36
第五章、數值實驗41
5.1 同步化41
5.2 安全通訊41
5.2.1 資訊訊號Amsin(20πt)，6種不同振幅41
5.2.2 加入不同的頻率之資訊訊號0.1sin(πt)和3.0sin(40πt)43
第六章、結論及後續研究66
6.1 結論66
6.2 後續研究67
參考文獻68
附錄72

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