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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 夏俊雄(Chun-Hsiung Hsia) | |
| dc.contributor.author | Shih-Hsin Chen | en |
| dc.contributor.author | 陳世昕 | zh_TW |
| dc.date.accessioned | 2021-06-17T04:27:00Z | - |
| dc.date.issued | 2020 | |
| dc.date.submitted | 2020-07-17 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70383 | - |
| dc.description.abstract | 本研究為關注雙向聯結之一階與二階藏本模型的同步化問題。在此兩模型中，每個粒子均只與標記號碼為前一個與後一個的粒子有交互作用，換句話說，第 i 個粒子只會與第 i + 1 與 i − 1 這兩個粒子有交互作用而已。在實際應用上，這種交互作用在電路學的串聯是很典型的設計。對於一階模型中，如果每個粒子的自然頻率均相同的情形下，我們首先證明了此模型具有全域的頻率同步。接著，針對初始粒子如果落在指定範圍內，我們提出了兩個相位同步的數學結果。而在每個粒子的自然頻率不完全相同的情形下，如果聯結的力夠大 (或是自然頻率彼此的差距不大)，且每個粒子初始均落在一個指定區域內，我們證明出此模型會達到頻率同步，同時我們也提供數值模擬來支持我們所推導出的數學理論。另一方面，我們發展出一套針對二階模型的頻率同步化理論。在此理論中我們證明出，如果連結力夠大、慣性項夠小以及所有粒子初始均落在一個指定範圍內的話，此二階模型會展現出頻率同步的結果。進一步地，如果這些粒子的自然頻率皆相同的話，我們也證明出此二階模型會有相位同步的結果。研究總結與未來相關問題也一併在文章中討論。 | zh_TW |
| dc.description.abstract | This article is concerned about the synchronization problem of the first order and the second order bidirectionally coupled Kuramoto model. In these two models, each oscillator only interacts with the oscillators with adjacent labelling numbers. Namely, the oscillator θi only inter-acts with θi+1 and θi-1. In real applications, this is a typical setting of concatenation connection. For the first order model, we first prove the global convergence of frequency synchronization for the identical os-cillators. Also, we present two results of phase synchronization for the identical case in relatively wide initial configuration regimes. In case that the coupling strength is sufficiently large (equivalent to the differ-ence of the natural frequencies is sufficiently small), we show that for non-identical oscillators within a suitable initial configuration regime, the first order bidirectionally coupled Kuramoto model exhibits a fre-quency synchronization. The supportive numerical simulations for the theories of the first order model are presented as well. On the other hand, we develop a frequency synchronization theory for the second or-der bidirectionally coupled Kuramoto model. We prove that this second order model exhibits the frequency synchronization for the non-identical oscillators if the coupling strength is sufficient large (equivalent to the difference of the natural frequencies is sufficiently small), the inertia is sufficiently small, and all oscillators are confined in a certain regime. In addition, we also show that this second order model exhibits the phase synchronization for the identical oscillators. Summary and several future works are discussed in this study as well. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T04:27:00Z (GMT). No. of bitstreams: 1 U0001-1707202013422400.pdf: 1752515 bytes, checksum: 15cacda3875c769c72d3eb9585c8472a (MD5) Previous issue date: 2020 | en |
| dc.description.tableofcontents | 口試委員審定書i 致謝ii 中文摘要iv Abstract v 1 Introduction 1 2 First Order Bidirectionally Coupled Kuramoto Model 11 2.1 Preliminaries and Main Results . . . . . . . . . . . . . . . . . . . . . 11 2.1.1 Phase and Frequency Synchronization for Identical Oscillators 14 2.1.2 Frequency Synchronization for Non-identical Oscillators . . . 15 2.2 Proof of Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2.1 Proof of Theorem 2.1.1–Theorem 2.1.3 . . . . . . . . . . . . . 22 2.2.2 Proof of Theorem 2.1.4 . . . . . . . . . . . . . . . . . . . . . . 27 2.3 Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.3.1 Simulation for Identical Oscillators . . . . . . . . . . . . . . . 38 2.3.2 Simulation for Non-identical Oscillators . . . . . . . . . . . . 40 3 Second Order Bidirectionally Coupled Kuramoto Model 44 3.1 Preliminaries and Main Results . . . . . . . . . . . . . . . . . . . . . 44 3.1.1 Frequency and Phase Synchronization . . . . . . . . . . . . . 47 3.1.2 Subfunction and Superfunction . . . . . . . . . . . . . . . . . 53 3.2 Proof of Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4 Conclusion 73 4.1 Summary of Main results . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5 Appendix 78 Bibliography 83 | |
| dc.language.iso | en | |
| dc.subject | 雙向交互作用 | zh_TW |
| dc.subject | 藏本模型 | zh_TW |
| dc.subject | 同步化 | zh_TW |
| dc.subject | synchronization | en |
| dc.subject | Kuramoto model | en |
| dc.subject | bidirectional interaction | en |
| dc.title | 雙向聯結之藏本模型的同步化數學分析 | zh_TW |
| dc.title | On Mathematical Analysis of Synchronization to Bidirectionally Coupled Kuramoto Oscillators | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 109-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 陳俊全(Chiun-Chuan Chen),薛名成(Ming-Cheng Shiue),黃信元(Hsin-Yuan Huang),陳怡全(Yi-Chiuan Chen) | |
| dc.subject.keyword | 同步化,藏本模型,雙向交互作用, | zh_TW |
| dc.subject.keyword | synchronization,Kuramoto model,bidirectional interaction, | en |
| dc.relation.page | 89 | |
| dc.identifier.doi | 10.6342/NTU202001598 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2020-07-20 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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