Publications
Detailed Information
On the asymptotic dynamics of particle and kinetic Kuramoto synchronization models : 쿠라모토 입자, 운동 동기화 모델의 점근적 동역학에 관하여
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 하승열 | - |
| dc.contributor.author | 박진영 | - |
| dc.date.accessioned | 2017-07-14T00:42:35Z | - |
| dc.date.available | 2017-07-14T00:42:35Z | - |
| dc.date.issued | 2016-08 | - |
| dc.identifier.other | 000000136304 | - |
| dc.identifier.uri | https://hdl.handle.net/10371/121314 | - |
| dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 8. 하승열. | - |
| dc.description.abstract | In this thesis, we study the Kuramoto model which describes the synchronous phenomena. In the Kuramoto model, the dynamics of the oscillators are presented by the intrinsic constant dynamics and the couplings between the oscillators. We study the sufficient conditions to achieve the emergence of synchronization for the Kuramoto model in various circumstances | - |
| dc.description.abstract | network structure, frustrations, heterogeneous intrinsic dynamics, inertia effects, etc. We also study the dynamics of the kinetic Kuramoto-Sakaguchi equation, which is the macroscopic description for the mean field limit of the Kuramoto model. | - |
| dc.description.tableofcontents | Chapter 1 Introduction 1
Chapter 2 Preliminaries 4 2.1 Synchronization 4 2.2 Derivation of the Kuramoto model 5 2.3 Kinetic Kuramoto model 6 2.4 Review on the previous literatures 6 Chapter 3 Complete synchronization 9 3.1 Basic key estimates 9 3.1.1 Dynamics of order parameters 10 3.1.2 Evolution of phase-diameter 17 3.2 Complete frequency synchronization 19 3.2.1 Identical oscillators 20 3.2.2 Nonidentical oscillators 25 Chapter 4 Kuramoto model on network with frustration 30 4.1 Previous results with uniform frustration 31 4.2 Dynamics of local order parameters 33 4.2.1 Local order parameters 33 4.2.2 Estimates of local order parameters 36 4.3 Complete synchronization with non-uniform frustration 38 4.4 Complete synchronization under reduced constraints 47 4.4.1 Estimate of the order parameters 48 4.4.2 Evolution of the phase-diameter 51 4.4.3 Dynamics of the order parameters 53 4.4.4 Emergence of complete synchronization 58 Chapter 5 Kuramoto model with heterogeneous dynamics 64 5.1 Practical synchronization and basic estimates 65 5.2 Practical synchronization with heterogeneous forcing 72 5.2.1 Bounded forcing 73 5.2.2 Unbounded forcing 78 Chapter 6 Interplay of inertia and heterogeneous dynamics 83 6.1 Heterogenous Kuramoto oscillators 83 6.1.1 Energy functional and main result 84 6.1.2 Energy estimates 87 6.1.3 The proof of Theorem 6.1.1 92 Chapter 7 Kuramoto model with adative coupling 95 7.1 Adaptive coupling 96 7.1.1 Elementary estimates 96 7.1.2 Frameworks and main results 101 7.1.3 Discussion on related works 102 7.2 Synchronization of a two-body system 103 7.2.1 Identical oscillators 104 7.2.2 Nonidentical oscillators 110 7.3 Synchronization estimate of a many-body system 112 7.3.1 Identical oscillators 112 7.3.2 Nonidentical oscillators 118 Chapter 8 Existence of BV-solution to the Kuramoto-Sakaguchi equation 122 8.1 Assumptions and basic properties 122 8.2 Global existence of BV weak solutions 127 8.2.1 Construction of approximate solutions 128 8.2.2 Several properties of the approximations 129 8.2.3 A global existence of weak solution 134 8.3 Exponentially growing solution 137 8.3.1 Construction of an exponentially growing mode 138 8.3.2 Dynamics of approximate solutions 140 8.4 Numerical simulations 152 8.4.1 Symmetric and monotone initial data 152 8.4.2 Non-symmetric initial data 156 Chapter 9 Synchronization of the Kuramoto-Sakaguchi equation 158 9.1 Synchronization of the identical Kuramoto-Sakaguchi equation 158 9.1.1 Dynamics of order parameters 160 9.1.2 Emergence of the complete synchronization 163 9.2 Positive invariant property of non-identical oscillators 166 Chapter 10 Conclusion and future works 180 Appendix 183 Appendix A Positivity of t_e and ε_θ in Lemma 4.4.6 183 Appendix B Proof of Lemma 5.2.3 188 Bibliography 191 국문 초록 199 | - |
| dc.format | application/pdf | - |
| dc.format.extent | 4493081 bytes | - |
| dc.format.medium | application/pdf | - |
| dc.language.iso | en | - |
| dc.publisher | 서울대학교 대학원 | - |
| dc.subject | Kuramoto model | - |
| dc.subject | kinetic equation | - |
| dc.subject | Kuramoto-Sakaguchi equation | - |
| dc.subject | synchronization | - |
| dc.subject | dynamical system | - |
| dc.subject.ddc | 510 | - |
| dc.title | On the asymptotic dynamics of particle and kinetic Kuramoto synchronization models | - |
| dc.title.alternative | 쿠라모토 입자, 운동 동기화 모델의 점근적 동역학에 관하여 | - |
| dc.type | Thesis | - |
| dc.contributor.AlternativeAuthor | Jinyeong Park | - |
| dc.description.degree | Doctor | - |
| dc.citation.pages | 198 | - |
| dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
| dc.date.awarded | 2016-08 | - |
- Appears in Collections:
- Files in This Item:
Item View & Download Count
Items in S-Space are protected by copyright, with all rights reserved, unless otherwise indicated.