EMERGENCE OF PARTIAL LOCKING STATES FROM THE ENSEMBLE OF WINFREE OSCILLATORS
- Title
- EMERGENCE OF PARTIAL LOCKING STATES FROM THE ENSEMBLE OF WINFREE OSCILLATORS
- Author
- 박진영
- Keywords
- The Kuramoto model; partial locking states; synchronization; the Winfree model
- Issue Date
- 2017-01
- Publisher
- BROWN UNIV
- Citation
- QUARTERLY OF APPLIED MATHEMATICS, v. 75, no. 1, page. 39-68
- Abstract
- We study the emergence of partial locking states for a subsystem whose dynamics is governed by the Winfree model. The Winfree model is the first mathematical model for synchronization. Thanks to the lack of conservation laws except for the number of oscillators, it exhibits diverse asymptotic nonlinear patterns such as partial and complete phase locking, partial and complete oscillator death, and incoherent states. In this paper, we present two sufficient frameworks for a majority sub-ensemble to evolve to the phase-locked state asymptotically. Our sufficient frameworks are characterized in terms of the mass ratio of the subsystem compared to the total system, ratio of the coupling strength to the natural frequencies, and the phase diameter of the subsystem. We also provide several numerical simulations and compare their results to the analytical results.
- URI
- http://www.ams.org/journals/qam/2017-75-01/S0033-569X-2016-01448-3/https://repository.hanyang.ac.kr/handle/20.500.11754/112484
- ISSN
- 0033-569X; 1552-4485
- DOI
- 10.1090/qam/1448
- Appears in Collections:
- COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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