Abstract
We discuss the asymptotic frequency synchronization for the non-identical Kuramoto oscillators with time delayed interactions. We provide explicit lower bound on the coupling strength and upper bound on the time delay in terms of initial congurations ensuring exponential synchronization. This generalizes not only the frequency synchronization estimate by Choi et al. [Phys. D, 241(7):735{ 754, 2012] for the non-identical Kuramoto oscillators without time delays but also improves previous [Automatica, 48(12):3008{3017, 2012] in the case of homogeneous time delays is assumed to be less than =2. The proof relies on a Lyapunov functional approach.
| Original language | English |
|---|---|
| Pages (from-to) | 1429-1445 |
| Number of pages | 17 |
| Journal | Communications in Mathematical Sciences |
| Volume | 19 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2021 |
Bibliographical note
Funding Information:Acknowledgments. Y.-P. Choi was supported by POSCO Science Fellowship of POSCO TJ Park Foundation and Yonsei University Research Fund of 2019-22-0212. C. Pignotti was supported by GNAMPA-INdAM and RIA-UNIVAQ. The authors also thank the anonymous referees for the careful reading of the paper and valuable comments.
Publisher Copyright:
© 2021 International Press
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics