Synchronization of Kuramoto oscillators with the distributed time-delays and inertia effect

Abstract

We prove the complete and partial phase synchronization for the Kuramoto oscillators with distributed time-delays and inertia effect. Our results assert that the Kuramoto models incorporated with a small variation of distributed time-delays and inertia effect still exhibit synchronization. This shows the robustness of the synchronization phenomena of the original Kuramoto model in the perturbation of time-delay and inertia effects. We also present several numerical experiments supporting our main results and exhibiting interesting patterns.

Keywords:

• Kuramoto model
• synchronization
• inertia effect
• distributed time-delays

AMS:

• Primary
• 34D06
• Secondary
• 34D05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

C.-H. H. was supported by the Ministry of Science and Technology ( MOST 109-2115-M-002 -013 -MY3) and National Center for Theoretical Sciences (NCTS), Taiwan. C.-Y. J. was supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (2018R1D1A1B07048325). B. K. was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of science, ICT and future planning (NRF-2020R1A2C1A01009184), and the UBSI Research Fund (project No.1.210114.01) of UNIST (Ulsan National Institute of Science & Technology). S. M. was supported by the National Research Foundation of Korea grant funded by the Korea government (MSIP) (NRF-2022R1C1C1003464).