Complete synchronization of Kuramoto oscillators with finite inertia

Young Pil Choi, Seung Yeal Ha, Seok Bae Yun

Research output: Contribution to journalArticlepeer-review

101 Citations (Scopus)


We present an approach based on Gronwall's inequalities for the asymptotic complete phasefrequency synchronization of Kuramoto oscillators with finite inertia. For given finite inertia and coupling strength, we present admissible classes of initial configurations and natural frequency distributions, which lead to the complete phasefrequency synchronization asymptotically. For this, we explicitly identify invariant regions for the Kuramoto flow, and derive second-order Gronwall's inequalities for the evolution of phase and frequency diameters. Our detailed time-decay estimates for phase and frequency diameters are independent of the number of oscillators. We also compare our analytical results with numerical simulations.

Original languageEnglish
Pages (from-to)32-44
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Issue number1
Publication statusPublished - 2011 Jan 1

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


Dive into the research topics of 'Complete synchronization of Kuramoto oscillators with finite inertia'. Together they form a unique fingerprint.

Cite this