Remarks on the nonlinear stability of the Kuramoto model with inertia

Young Pil Choi, Seung Yeal Ha, Se Eun Noh

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10 Citations (Scopus)


In this short note, we present an a priori nonlinear stability estimate for the Kuramoto model with finite inertia in ℓ∞-norm under some a priori condition on the size of the phase diameter. As a direct corollary of our nonlinear stability estimate, we show that phase-locked states obtained in Choi, Ha, and Yun (2011) are orbital-stable in ℓ∞-norm, which means that the perturbed phase-locked state approaches the phase-shift of the given phase-locked state. The phase-shift is explicitly determined by the averages of initial phase and frequency distribution and the strength of inertia m.

Original languageEnglish
Pages (from-to)391-399
Number of pages9
JournalQuarterly of Applied Mathematics
Issue number2
Publication statusPublished - 2015

Bibliographical note

Publisher Copyright:
© 2015 Brown University.

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


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