Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 268, Issue 12, Pages 7897-7939Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2019.11.090
Keywords
Kuramoto model; Frequency synchronization; Phase synchronization; Time-delay interactions; Phase lag; Complete and partial synchronization
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Funding
- Basic Science Research Program through the National Research Foundation of Korea - Ministry of Education [2018R1D1A1B07048325]
- UNIST (Ulsan National Institute of Science and Technology) [1.170045.01]
- Basic Science Research Program through the National Research Foundation of Korea (NRF) - Ministry of Science, ICT and Future Planning [NRF-2017R1E1A1A03070406]
- Ministry of Science and Technology, Taiwan [MOST 107-2918-I-002-009, MOST 107-2115-M-002-006-MY2]
- NRF of Korea
- Japan Society for the Promotion of Science [18K03369]
- Grants-in-Aid for Scientific Research [18K03369] Funding Source: KAKEN
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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. (C) 2019 Elsevier Inc. All rights reserved.
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