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  • Open Access

Discontinuous transition to synchrony in the Kuramoto-Sakaguchi model with a uniform distribution of frequencies

A. Pikovsky*

  • Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam-Golm, Germany

  • *Contact author: pikovsky@uni-potsdam.de
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APS Open Sci. 1, 000030 – Published 28 May, 2026

DOI: https://doi.org/10.1103/lfvq-b68c

Abstract

The transition to synchrony in the Kuramoto model of globally coupled phase oscillators with a uniform distribution of natural frequencies is discontinuous. We extend the theory of this transition to the Kuramoto-Sakaguchi model, taking into account a phase shift in coupling. In the thermodynamic limit, we derive dependencies of the order parameters on the coupling strength and the phase shift, and describe two transitions from disorder to partial synchrony and from partial synchrony to complete synchrony. In all cases, the first transition is discontinuous, although for phase shifts close to π/2, the jump is exponentially small. We also discuss which properties of the transition hold for distributions close to the uniform one.

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APS Open Sci. 1, 000030– Published 28 May, 2026
Vol. 1
  • Received 12 April 2026
  • Revised 16 May 2026
  • Accepted 20 May 2026
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