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  • Open Access

Effects of inertia on the asynchronous state of a disordered Kuramoto model

Yagmur Kati1,2,*, Ralf Toenjes1, and Benjamin Lindner1,2

  • *Contact author: yagmur.kati@hu-berlin.de
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Phys. Rev. E 112, 044301 – Published 6 October, 2025

DOI: https://doi.org/10.1103/xt4m-bkp8

Abstract

We investigate the role of inertia in the asynchronous state of a disordered Kuramoto model. We extend an iterative simulation scheme to the case of the Kuramoto model with inertia in order to determine the self-consistent fluctuation statistics, specifically, the power spectra of network noise and single oscillators. Comparison with network simulations demonstrates that this works well whenever the system is in an asynchronous state. We also find an unexpected effect when varying the degree of inertia: the correlation time of the oscillators becomes minimal at an intermediate mass of the oscillators; correspondingly, the power spectra appear flatter and thus more similar to white noise around the same value of mass. We also find a similar effect for the Lyapunov spectra of the oscillators when the mass is varied.

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Phys. Rev. E 112, 044301– Published 6 October, 2025
  • Received 11 March 2025
  • Accepted 15 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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