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Kwon, Bongsuk
Partial Differential Equations and their applications
Research Interests
  • Partial differential equations, hyperbolic conservation laws, stability of nonlinear waves

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ON THE GLOBAL CONVERGENCE OF FREQUENCY SYNCHRONIZATION FOR KURAMOTO AND WINFREE OSCILLATORS

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Title
ON THE GLOBAL CONVERGENCE OF FREQUENCY SYNCHRONIZATION FOR KURAMOTO AND WINFREE OSCILLATORS
Author
Hsia, Chun-HsiungJung, Chang-YeolKwon, Bongsuk
Issue Date
2019-07
Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
Citation
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v.24, no.7, pp.3319 - 3334
Abstract
We investigate the collective behavior of synchrony for the Kuramoto and Winfree models. We first prove the global convergence of frequency synchronization for the non-identical Kuramoto system of three oscillators. It is shown that the uniform boundedness of the diameter of the phase functions implies complete frequency synchronization. In light of this, we show, under a suitable condition on the coupling strength and deviation of the intrinsic frequencies, that the diameter function of the phases is uniformly bounded. In a similar spirit, we also prove the global convergence of phase-locked synchronization for the Winfree model of N oscillators for N >= 2.
URI
https://scholarworks.unist.ac.kr/handle/201301/27340
URL
http://aimsciences.org//article/doi/10.3934/dcdsb.2018322
DOI
10.3934/dcdsb.2018322
ISSN
1531-3492
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