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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Hsia, Chun-Hsiung^1,2  Jung, Chang-Yeol³  Kwon, Bongsuk³  Ueda, Yoshihiro⁴ 

[1] Natl Taiwan Univ, Inst Appl Math Sci, Dept Math, Taipei, Taiwan

[2] Natl Taiwan Univ, Natl Ctr Theoret Sci, Taipei, Taiwan

[3] Ulsan Natl Inst Sci & Technol, Dept Math Sci, Ulsan, South Korea

[4] Kobe Univ, Maritime Sci, Kobe, Hyogo, Japan

关键词: Kuramoto model;    Frequency synchronization;    Phase synchronization;    Time-delay interactions;    Phase lag;    Complete and partial synchronization;   

DOI  :  10.1016/j.jde.2019.11.090

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free