Synchronization in Networks of Coupled Phase Oscillators: From Designing for Robustness to Exploring Emergent Patterns
Synchronization in Networks of Coupled Phase Oscillators: From Designing for Robustness to Exploring Emergent Patterns
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211152715
- ISBN
- 9798384053255
- DDC
- 519
- 서명/저자
- Synchronization in Networks of Coupled Phase Oscillators: From Designing for Robustness to Exploring Emergent Patterns
- 발행사항
- [Sl] : Cornell University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 112 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-03, Section: B.
- 주기사항
- Advisor: Anderson, Catherine.
- 학위논문주기
- Thesis (Ph.D.)--Cornell University, 2024.
- 초록/해제
- 요약Networks of coupled phase oscillators have been used to model a wide array of applications including circadian rhythms, flashing fireflies, Josephson junction arrays, and high-voltage electric grids. In many of these applications, synchronization is a behavior that emerges over time and is of interest to understand and optimize for. This thesis uses tools from both pure and applied mathematics to address some of the key challenges in network theory as they relate to synchronization in networks of coupled phase oscillators via two lines of research. In the first line of research, we propose a mathematical model for designing robust networks of coupled phase oscillators by leveraging a vulnerability measure that quantifies the impact of a small perturbation at an individual phase oscillator's natural frequency on the system's global synchronized frequencies. We apply this mathematical framework to design high-voltage electric grids that are robust to the integration of renewable energy. In the second line of research, we use graphon theory to outline conditions under which synchronization emerges on large random networks of coupled phase oscillators. In particular, we consider the Kuramoto model on Erdos-Renyi networks and show ´ that the model will phase synchronize with high probability as the size of the network, n, tends to infinity, as long as the edge probability is asymptotically larger than the connectivity threshold, log(n)/ n. We also consider the Sakaguchi-Kuramoto model on Erdos-Renyi networks and show that this model will frequency synchronize with high probability as n tends to infinity, as long as the edge probability is a constant greater than zero.
- 일반주제명
- Applied mathematics
- 일반주제명
- Mathematics
- 일반주제명
- Computer science
- 일반주제명
- Alternative energy
- 키워드
- Networks
- 키워드
- Synchronization
- 키워드
- Edge probability
- 키워드
- Vulnerability
- 기타저자
- Cornell University Applied Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■1001 ▼aNagpal, Shriya Vedantham.▼0(orcid)0000-0003-3151-7574
■24510▼aSynchronization in Networks of Coupled Phase Oscillators: From Designing for Robustness to Exploring Emergent Patterns
■260 ▼a[Sl]▼bCornell University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a112 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-03, Section: B.
■500 ▼aAdvisor: Anderson, Catherine.
■5021 ▼aThesis (Ph.D.)--Cornell University, 2024.
■520 ▼aNetworks of coupled phase oscillators have been used to model a wide array of applications including circadian rhythms, flashing fireflies, Josephson junction arrays, and high-voltage electric grids. In many of these applications, synchronization is a behavior that emerges over time and is of interest to understand and optimize for. This thesis uses tools from both pure and applied mathematics to address some of the key challenges in network theory as they relate to synchronization in networks of coupled phase oscillators via two lines of research. In the first line of research, we propose a mathematical model for designing robust networks of coupled phase oscillators by leveraging a vulnerability measure that quantifies the impact of a small perturbation at an individual phase oscillator's natural frequency on the system's global synchronized frequencies. We apply this mathematical framework to design high-voltage electric grids that are robust to the integration of renewable energy. In the second line of research, we use graphon theory to outline conditions under which synchronization emerges on large random networks of coupled phase oscillators. In particular, we consider the Kuramoto model on Erdos-Renyi networks and show ´ that the model will phase synchronize with high probability as the size of the network, n, tends to infinity, as long as the edge probability is asymptotically larger than the connectivity threshold, log(n)/ n. We also consider the Sakaguchi-Kuramoto model on Erdos-Renyi networks and show that this model will frequency synchronize with high probability as n tends to infinity, as long as the edge probability is a constant greater than zero.
■590 ▼aSchool code: 0058.
■650 4▼aApplied mathematics
■650 4▼aMathematics
■650 4▼aComputer science
■650 4▼aAlternative energy
■653 ▼aDynamical systems
■653 ▼aNetworks
■653 ▼aSynchronization
■653 ▼aEdge probability
■653 ▼aVulnerability
■690 ▼a0364
■690 ▼a0405
■690 ▼a0984
■690 ▼a0363
■71020▼aCornell University▼bApplied Mathematics.
■7730 ▼tDissertations Abstracts International▼g86-03B.
■790 ▼a0058
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17163495▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
