Event
01_1
| 제출번호(No.) | 0058 |
|---|---|
| 분류(Section) | Poster Session |
| 분과(Session) | Applied Mathematics (AM) |
| 영문제목 (Title(Eng.)) |
Emergent dynamics of Kuramoto oscillators with adaptive couplings: conservation law and fast learning |
| 저자(Author(s)) |
Seung-yeal Ha1, Jaeseung Lee1, Zhuchun Li2, Jinyeong Park3 Seoul National University1, Harbin Institute of Technology2, University of Granada3 |
| 초록본문(Abstract) | We study an emergent dynamics of the Kuramoto oscillators with adaptive couplings. For the Kuramoto model, pairwise coupling strengths are assumed to be constants and uniform over all interaction pairs. This might not be reasonable for real applications. In this paper, we relax this uniform strength ansatz by adopting a dynamic feedback law depending on the relative phase differences, and discuss two Kuramoto type models with adaptive couplings. As a first adaptive model, we consider the adaptive law introduced by Picallo and Riecke, and present several sufficient frameworks leading to the asymptotic synchronization. For the second model with an adaptive coupling law, we consider the Model A introduced in the previous work. For this model, we introduce a small parameter that diversifies time scales for the dynamics of the states of a model. In this fast-slow setting, coupling strengths become the fast variables, whereas the phase dynamics becomes the slow one. Tikhonov's theorem guarantees the convergence of slow-fast dynamical system to a Kuramoto type model in this singular limit. We also classify admissible phase-locked states for the limit system, and provide a sufficient framework leading to the complete phase synchronization, in which all oscillators' phase are aggregated to a common phase. |
| 분류기호 (MSC number(s)) |
70F99, 92B25 |
| 키워드(Keyword(s)) | adaptive coupling, complete synchronization, Kuramoto model, slow-fast dynamics, Tikhonov singular perturbation theory |
| 강연 형태 (Language of Session (Talk)) |
English |