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研究生:林寬展
研究生(外文):Kuan-Jhan Lin
論文名稱:三個倉本模型的振盪粒子在時間延遲效果下頻率同步的全局收斂性
論文名稱(外文):On the global convergence of frequency synchronization for three Kuramoto oscillators under time-delay effect
指導教授:夏俊雄
指導教授(外文):Chun-Hsiung Hsia
口試委員:陳俊全黃信元薛名成陳怡全
口試委員(外文):Chiun-Chuan ChenHsin-Yuan HuangMing-Cheng ShiueYi-Chiuan Chen
口試日期:2020-07-09
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2020
畢業學年度:108
語文別:英文
論文頁數:45
中文關鍵詞:倉本模型同步化時間延遲全局收斂性振盪粒子
外文關鍵詞:Kuramoto modelsynchronizationtime-delayglobal convergenceoscillator
DOI:10.6342/NTU202001906
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本論文研究了在時間延遲下之倉本模型的集體同步行為。 倉本模型已被大規模用來研究耦合振盪粒子的同步行為。 其成果被應用在諸如物理學、生物學以及網絡等廣泛的科學學科中。經典的倉本模型假定振盪粒子之間的相互作用是瞬時的。 但是,在現實世界的系統中,粒子之間的交互作用並不是瞬時的,因為我們必須考慮信號傳播時間和決策過程。 因此,考慮時間延遲模型是很自然的。 例如,在神經網絡以及鐳射和微波振盪器的陣列中,突觸、樹突和傳播延遲都是必須被考慮的。 本論文的主要結論是在自然頻率相同的情況下,三個倉本模型的振盪粒子在時間延遲效果下頻率同步的全局收斂性。
The thesis studies the collective behavior of synchrony for the full-delay Kuramoto model. The Kuramoto model has been studied for the synchronization behavior of coupled oscillators. It is also applied in widely scientific disciplines such as physics, biology and networks etc. The classical Kuramoto model assumes that the interactions between oscillators are instantaneous. However, in the real-world systems, the interactions between the elements are not instantaneous since we have to take signal propagation time and decision making process into consideration. Hence it is natural to consider the time delay model. For examples, in the neural networks, and also in the arrays of lasers and microwave oscillators, the synaptic, dendritic, and propagation delays must be taken into account. The main conclusion of this thesis is the global convergence of frequency synchronization for three Kuramoto oscillators under time-delay effect in the identical case.
口試委員會審定書……………………………………………………………………i
誌謝…………………………………………………………………………………...ii
中文摘要……………………………………………………………………………..iii
英文摘要……………………………………………………………………………..iv
第一章:Introduction………………………………………………………………….1
第二章:Main result and Proof………………………………………………………9
第三章:Conclusion………………………………………………………………….38
參考文獻…………………………………………………………………….………43
[1]Hsia, Chun-Hsiung; Jung, Chang-Yeol; Kwon, Bongsuk; Ueda, Yoshihiro,Synchronization of Kuramoto oscillators with time-delayed interactions and phase lag effect,J. Differential Equations, 268 (2020), no. 12, 7897-7939.

[2]Hsia, Chun-Hsiung; Jung, Chang-Yeol; Kwon, Bongsuk,On the global convergence of frequency synchronization for Kuramoto and Winfree oscillators,Discrete Contin. Dyn. Syst. Ser. B 24 (2019), no. 7, 3319-3334.

[3]
Hsia, Chun-Hsiung; Jung, Chang-Yeol; Kwon, Bongsuk,On the synchronization theory of Kuramoto oscillators under the effect of inertia,J. Differential Equations 267(2019), no. 2, 742-775.

[4]Y. Kuramoto,Self-entrainment of a population of coupled non-linear oscillators,in: International Symposium on Mathematical Problems in Theoretical Physics,in: Lecture Notes in Phys., vol.39, Springer, New York, 1975, pp.420-422.

[5]Y. Kuramoto,Chemical Oscillations, Waves and Turbulence,Springer-Verlag, Berlin, 1984.

[6]S. H. Strogatz,From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators,Physica D, 143 (2000), 1-20.

[7]Arkady Pikovsky, Michael Rosenblum, Jürgen Kurths,Synchronization. A universal concept in nonlinear sciences,Cambridge University Press (2001).

[8] Steven Strogatz,Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life,Hachette Books (2003).

[9]Y.-P. Choi, S.-Y. Ha, S. Jung and Y. Kim,Asymptotic formation and orbital stability of phase-locked states for the Kuramoto model,Physica D, 241 (2012), 735-754.

[10]S.-Y. Ha, H. K. Kim and S. W. Ryoo,Emergence of phase-locked states for the Kuramoto model in a large coupling regime,Commun. Math. Sci., 14 (2016), 1073-1091.

[11]S.-Y. Ha, T. Ha, J.-H. Kim,On the complete synchronization of the Kuramoto phase model,Physica D 239(17) (2010) 1692-1700.

[12]F. D$\ddot{o}$rfler and F. Bullo,Synchronization in Complex Networks of Phase Oscillators: A Survey,Automatica, 50 (2014), 1539-1564.

[13]F. D$\ddot{o}$rfler, F. Bullo,On the critical coupling for Kuramoto oscillators,
SIAM J. Appl. Dyn. Syst. 10(3) (2011) 1070-1099.
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