臺灣博碩士論文加值系統

摘 要

渾沌現象普遍存在於宇宙之間，大至星際，小至原子。本文研究耦合之量子點胞。將它們用於量子點胞自動機，以構成神經胞網路。即使只有兩個量子點胞，亦可因胞間極化與基底之些許差異而產生渾沌運動。研究此種奈米尺寸之渾沌運動對於未來超小型非線性胞網路之製成及用標準的非線性胞網路硬體有效地進行量子計算都是非常重要的。作為前瞻性的研究，本文將對此系統作全面之研究，研究重點為：
1. 系統渾沌行為之研究。用相圖、功率頻譜圖、參數圖及李亞普諾夫指數分析超渾沌之行為。
2. 系統之渾沌控制。利用外加常值項、GYC控制理論、實用適應控制、可變結構控制、脈衝控制及最佳控制將渾沌運動控制到週期運動或平衡態，同樣地可將規則運動渾沌化。
3.系統之渾沌同步。利用非線性控制、線性耦合、GYC控制理論、可變參數線性耦合實用適應控制、實用適應控制、可變結構控制、最佳控制及脈衝控制方法研究渾沌同步。

Abstract
Chaos exists everywhere in the universe, from interstellar space to interatomic interval. In this thesis, coupled quantum-dot cells will be studied. They are used for Quantum-dots Cellular Automata (QCA), to build Cellular Neural Networks (CNN). It is shown that the connection of even only two quantum-dot cells can cause the onset of chaotic motion by small difference of polarizations and template between cells. This study could be very important for future ultra-small realization of CNNs and, on the other hand, for performing quantum computation efficiently via hardware by using standard CNN. As a foresighted study, a detailed study of this system will be developed. The main parts of our study are:
1. The study of chaotic system: By phase portraits, power spectra, parameter diagram and Lyapunov exponents, the various chaotic behaviors of this hyperchaos system are studied.
2. Chaos control and chaotization for the system: By addition of constant term, by GYC control, by pragmatical adaptive control, by variable structure control, by impulsive control and by optimal control, the chaotic motions of the system can be controlled to periodic motions or to equilibrium states, as well as the regular motions of the system can be chaotized.
3. Chaos synchronization for the system: By nonlinear control, by linear coupling, by GYC control, by variable parameters linear couple pragmatical adaptive control, by pragmatical adaptive control, by variable structure control, by impulsive control and by optimal control, the synchronization of the chaos motions of the two systems are studied.

Contents

Abstract i
誌 謝 iv
Contents v
List of Figures ix
List of Tables xiii
Chapter 1 Introduction 1
Chapter 2 Bounded and Unbounded Chaos 5
2-1 Preliminary 5
2-2 Bounded Chaos 5
2-3 Unbounded Chaos 7
Chapter 3 Chaos Control and Chaotization 13
3-1 Preliminary 13
3-2 Chaos Control of the Quantum-CNN Systems 13
3-2-1 Model of Two Quantum-CNN Oscillator Systems 14
3-2-2 Controlling Quantum-CNN attractor to equilibrium 14
3-3 Chaos Control of Quantum-CNN Oscillators Chaotic System by Variable Structure Control 23
3-4 Chaos control of Quantum-CNN Oscillators Chaotic System by Impulse Control 25
3-5 Chaotization of Quantum-CNN Chaotic System by Optimum Control 26
Chapter 4 Generalized and Symplectic Synchronizations 28
4-1 Preliminary 28
4-2 The Generalized Synchronization of a Quantum-CNN Chaotic Oscillator with Different Order Systems 29
4-2-1 Generalized Synchronization Scheme 29
4-2-2 Numerical Results of the Generalized Chaos Synchronization of the Quantum-CNN Oscillator with Different Order Systems 31
4-3 The Generalized Synchronization of a Quantum-CNN Chaotic Oscillator with a Double Duffing Chaotic System 40
4-3-1 Generalized Synchronization Scheme 40
4-3-2 Numerical Results of Generalized Chaos Synchronization of the Quantum-CNN Oscillator with a Double Duffing Chaotic Systems 41
4-4 Symplectic Synchronization of Different Chaotic Systems 51
4-4-1 Symplectic Synchronization Scheme 51
4-4-2 Numerical Results for the Symplectic Chaos Synchronization of Quantum-CNN Oscillator and Rössler System 52
4-5 Chaos Synchronization of Quantum-CNN Oscillators Chaotic System by Variable Structure Control 62
Chapter 5 Linear Coupling Synchronization 67
5-1 Preliminaries 67
5-2 Synchronization of the Complex Chaotic Systems in Series Expansion Form 67
5-2-1 Synchronization Schemes of Complex Chaotic Systems in Series Expansion Form 67
5-2-2 Numerical Results of the Synchronization of Two Quantum-CNN Oscillator Systems by Unidirectional and by Mutual Linear Coupling 69
5-3 Chaos Synchronization of Complex Chaotic Systems in Series Form by Optimal control 83
5-3-1 Linearly Coupled Chaos Synchronization Scheme by Optimum Control 83
5-3-2 Numerical Results of the Synchronization of Two Quantum-CNN Oscillator Systems by Unidirectional and by Mutual Linear Coupling 85
5-4 Chaos Synchronization of Quantum-CNN Chaotic System by Impulse Control 92
Chapter 6 Pragmatical Synchronization and Control 95
6-1 Preliminary 95
6-2 Pragmatical Generalized Synchronization of Chaotic Systems with Uncertain Parameters by Adaptive Control 96
6-2-1 Pragmatical Generalized Synchronization Scheme by Adaptive Control 97
6-2-2 Numerical Results of Pragmatical Generalized Chaos Synchronization of Two Quantum-CNN Oscillators by Adaptive Control 98
6-3 Pragmatical Adaptive Control for Different Chaotic Systems 106
6-3-1 Pragmatical Adaptive Control Scheme 106
6-3-2 Numerical Results of the Chaos Control 107
6-4 Synchronization of Chaotic System with Uncertain Variable/Chaotic Parameters by Linear Coupling and Pragmatical Adaptive Tracking 115
6-4-1 Theoretical Analyses 115
6-4-2 Numerical Examples 119
Chapter 7 Chaos Control, Chaotization and Synchronization by GYC Partial Region Stability Theory 143
7-1 Preliminary 143
7-2 Chaos Control and Chaotization of Chaotic System to Different Systems 143
7-2-1 Chaos Control and Chaotization Scheme 143
7-2-2 Numerical Results of the Chaos Control 144
7-3 The Chaos Generalized Synchronization of a Quantum-CNN Chaotic Oscillator with a Double Duffing Chaotic System 149
7-3-1 Chaos Generalized Synchronization Strategy 149
7-3-2 Numerical Simulations 150
Chapter 8 Conclusions 159
Appendix A GYC Pragmatical Asymptotical Stability Theorem 163
Appendix B GYC Partial Region Stability Theory 166
References 172
Paper List 182

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