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研究生:詹祐毓
研究生(外文):You-Yu Jan
論文名稱:數位混沌系統核心函數之設計
論文名稱(外文):Kernel Function Design for Digital Chaotic Systems
指導教授:孫郁興孫郁興引用關係盧樹台
指導教授(外文):Yuh-Sien SunShuh-Tai Lu
學位類別:碩士
校院名稱:清雲科技大學
系所名稱:電子工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:94
語文別:中文
論文頁數:84
中文關鍵詞:Chua’s混沌系統羅倫茲混沌系統核心函數安全通訊奇異吸引子
外文關鍵詞:Chua’s chaotic systemLorenz chaotic systemkernel functionssecurity communicationstrange attractor
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混沌理論在近期已受到廣大的運用,混沌信號能被利用來處理或分析各種工程問題,例如混沌信號可應用在通訊領域中,使用混沌信號來取代隨機信號,將傳輸資料作遮蔽或調變來達到安全通訊目的。如何獲得更複雜的非線性混沌系統函數,則是研究學者欲研究的方向,本論文的研究方向主要是根據類比Chua’s混沌系統的狀態方程,將其數位化後,加入數種非線性的核心函數,藉由非線性核心函數的特性增加不可預測的擾動,以獲得更複雜的混沌效果。這些非線性核心函數亦可成功運用於羅倫茲混沌系統中。新混沌系統的參數適用範圍,及運用混沌狀態的雙奇異吸引子特性以電腦演算法判定亦於本文中提出,且本文所設計的混沌系統能具有同步收斂的作用。
The chaotic theory has already been applied to many fields recently. The chaotic signal can be used to process or analyze various kinds of engineering problems. For example, the chaotic signal can be applied to the communication domain. In a security communication, the chaotic signal is always used to replace the random signal generator which masks and modulates the transmitted data. To find out more complicated nonlinear chaotic system functions is an important topic for researchers. This thesis focus on how to improve the state equation of analog Chua’s chaotic system and to digitize the Chua’s chaotic system into several kinds of nonlinear kernel functions. Based on those nonlinear characteristic kernel functions, it is able to increase the unpredictable perturbation and obtain more complicated chaotic result. Those nonlinear kernel functions can be successfully applied to Lorenz chaotic system also. The parameters available range and the algorithm of identifying chaos strange attractor characteristic are depicted in this thesis. The synchronization convergence actions of all designed chaotic systems are proved also.
中文摘要 ................................................. i
英文摘要 ................................................. ii
誌謝 ..................................................... iii
目錄 ..................................................... iv
表目錄 .................................................... vi
圖目錄 .................................................... vii
第一章 前言 ................................................ 1
1.1研究背景及動機........................................... 1
1.2論文貢獻................................................. 3
1.3論文概述................................................. 4
第二章 混沌系統.............................................. 5
2.1混沌介紹 ................................................. 5
2.1.1混沌運動具有的特性....................................... 5
2.1.2顯示混沌現象的簡單方法.................................... 7
2.2 Chua’s混沌系統.......................................... 9
2.2.1 Chua’s電路非線性函數................................... 11
2.2.2 Chua’s電路的混沌狀態................................... 12
2.3羅倫茲混沌系統............................................. 16
2.4混沌系統的應用............................................. 20
第三章 混沌系統核心函數設計..................................... 23
3.1 Chua’s混沌系統核心函數設計之選擇........................... 23
3.2加入-atan(x)函數之Chua’s混沌系統........................... 26
3.3加入-sin(x)函數之Chua’s混沌系統............................ 30
3.4加入-atan(x)及-sin(x)函數之Chua’s混沌系統................... 36
3.5加入-sin(x)函數之羅倫茲混沌系統............................. 40
3.6加入-atan(x)函數之羅倫茲混沌系統............................. 44
3.7混沌信號頻譜分析............................................ 46
第四章 混沌系統實驗結果......................................... 51
4.1混沌系統之同步.............................................. 51
4.2 Chua’s數位混沌系統參數有效範圍與混沌狀態.................... 61
4.2.1判斷混沌狀態之演算法...................................... 61
4.2.2 Chua’s混沌系統參數適用值................................. 62
4.2.3加入-atan(x)之Chua’s混沌系統參數適用值..................... 69
4.2.4加入-sin(x)之Chua’s混沌系統參數適用值...................... 72
4.2.5加入-sin(x)與-atan(x)之Chua’s混沌系統參數適用值............ 75
4.3羅倫茲混沌系統參數有效範圍與混沌狀態........................... 79
第五章 結論與未來展望........................................... 81
參考文獻 ..................................................... 82
簡歷.......................................................... 84
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