臺灣博碩士論文加值系統

本篇論文探討有關整數階與分數階變革式心搏系統的渾沌、渾沌同步及其反控制。藉由相圖、龐卡萊圖及分歧圖等數值模擬結果，可以得知週期及渾沌的現象。另外經由參數激發法使得兩個非耦合的整數階或分數階變革式心搏系統達到同步。並透過外加常數項或非線性項獲得分數階變革式心搏系統的反控制。最後，成功的利用參數激發的方式，讓整數階與分數階的變革式心搏系統達到渾沌化。

Chaos, chaos synchronization and anticontrol for integral and fractional modified heartbeat systems are studied in the thesis. By applying numerical results, phase portrait, Poincaré maps and bifurcation diagrams, a variety of the phenomena of the periodic and chaotic motion can be presented. The synchronizations of two uncoupled integral and fractional order chaotic modified heartbeat systems are accomplished by parameter excited synchronization. Anticontrol of chaos of fractional order modified heartbeat systems can be obtained by addition of a constant term and addition of a nonlinear term. Chaotization of integral and fractional order modified heartbeat systems by parameter excited method, replacement of the parameter of first system by the function of the chaotic state variables of a second chaotic system, is successfully accomplished.

ABSTRACT i
ACKNOWLEDGMEMT ii
CONTENTS iii
LIST OF FIGURES iv
Chapter 1 Introduction 1

Chapter 2 A Fractional Derivative and a Modified Heartbeat System 3
2.1 A fractional derivative and its approximation 3
2.2 A modified heartbeat system and the corresponding fractional order system 4

Chapter 3 Chaos in a Modified Heartbeat System and in Its Fractional order Systems 6
3.1 Chaos in a integral order modified heartbeat system 6
3.2 Chaos in a fractional order modified heartbeat system 6

Chapter 4 Parameter Excited Chaos Synchronizations of Integral and Fractional Order Modified Heartbeat Systems 39
4.1 The scheme of parameter excited chaos synchronizations 39
4.2 Parameter Excited Chaos Synchronization by kcosx、kcosy、kcosxcosy 40
4.2.1 Parameter Excited Chaos Synchronizations by kcosx 40
4.2.2 Parameter Excited Chaos Synchronizations by kcosy 41
4.2.3 Parameter Excited Chaos Synchronizations by kcosxcosy 41

Chapter 5 Anticontrol of Chaos of the Fractional Order Modified Heartbeat Systems 73
5.1 Anticontrol of Chaos by addition of a constant term 73
5.2 Anticontrol of Chaos by addition of a nonlinear term 74

Chapter 6 Parameter Excited Chaotization of Integral and Fractional Order Modified Heartbeat Systems 89
6.1 A nano resonator system and the chaotization scheme 89
6.2 Chaotization by parameter excited method 90
6.2.1 Chaotization of a integral order modified heartbeat system 90
6.2.2 Chaotization of a fraction order modified heartbeat system 91

Chapter 7 Conclusions 103

REFERENCES 105

APPENDIX 112

PAPER LIST 113

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