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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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Synchronization of Kuramoto oscillators with time-delayed interactions and phase lag effect

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Title
Synchronization of Kuramoto oscillators with time-delayed interactions and phase lag effect
Author
Hsia, Chun-HsiungJung, Chang-YeolKwon, BongsukUeda, Yoshihiro
Issue Date
2020-06
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation
JOURNAL OF DIFFERENTIAL EQUATIONS, v.268, no.12, pp.7897 - 7939
Abstract
We investigate the synchronized collective behavior of the Kuramoto oscillators with time-delayed interactions and phase lag effect. Both the phase and frequency synchronization are in view. We first prove the frequency synchronization for both semi-delay and full-delay models with heterogeneous time-delays and phase lags. We also prove the complete and partial phase synchronization for both models with the uniform time-delay and phase lag. Our results show that the Kuramoto models incorporated with small variation of time-delays and/or phase lag effect still exhibit the synchronization. These support that the original Kuramoto model (i.e., no time-delays/phase lags) is qualitatively robust in the perturbation of time-delay and phase lag effects. We also present several numerical experiments supporting our main results. © 2019 Elsevier Inc.
URI
https://scholarworks.unist.ac.kr/handle/201301/31227
URL
https://www.sciencedirect.com/science/article/pii/S0022039619306242?via%3Dihub
DOI
10.1016/j.jde.2019.11.090
ISSN
0022-0396
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