中文摘要
本篇論文主要是探討在耦合矩陣具有週期邊界條件的情況下，小波變換理論會如何影響一個耦合混沌系統的主值穩定函數。在本篇論文裡，我們選取了四種典型的非線性耦合混沌系統，並呈獻在不同大小的耦合矩陣下，四種系統經過小波變換前後的不同數值結果。

Abstract
The largest Lyapunov exponent of the synchronization manifold in coupled chaotic systems is called the master stability function MSF. MSF is an effective tool to study the synchronous phenomena in coupled chaotic systems. In this thesis, the influence of the wavelet transform method on MSFs are discussed for the coupling matrix G with periodic boundary conditions. First, we clarify a necessary and sufficient condition for local synchronized in coupled chaotic systems. Moreover, the synchronous interval is analytically indicated for coupled chaotic systems. Then, the four typical nonlinear coupled chaotic systems: Rössler system, Lorenz System, Chua's Circuit System, and HR Neuron are numerically presented to verify our theoretical results for several oscillators with periodic boundary conditions. Finally, the wavelet parameter α is selected to illustrate its corresponding synchronous interval.

Contents
Abstract .......................................... 1
1. Introduction ................................... 1
2. Preliminary .................................... 6
3. Synchronization Interval Based on MSFs ......... 11
4. Numerical Results .............................. 14
5. Conclusion ..................................... 55
6. References ..................................... 56
7. Appendix ....................................... 58

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