Synchronization of Kuramoto oscillators with time-delayed interactions and phase lag effect
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- Synchronization of Kuramoto oscillators with time-delayed interactions and phase lag effect
- Hsia, Chun-Hsiung; Jung, Chang-Yeol; Kwon, Bongsuk; Ueda, Yoshihiro
- Issue Date
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- JOURNAL OF DIFFERENTIAL EQUATIONS, v.268, no.12, pp.7897 - 7939
- 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.
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