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  • Letter
  • Open Access

Generic criterion for explosive synchronization in heterogeneous phase oscillator populations

Can Xu1,*, Xuan Wang1, and Per Sebastian Skardal2,†

  • 1Institute of Systems Science and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
  • 2Department of Mathematics, Trinity College, Hartford, Connecticut 06106, USA

  • *xucan@hqu.edu.cn
  • †persebastian.skardal@trincoll.edu
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Phys. Rev. Research 4, L032033 – Published 22 August, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L032033

Abstract

Ordered and disordered behavior in large ensembles of coupled oscillators map to different functional states in a wide range of applications, e.g., active and resting states in the brain and stable and unstable power grid configurations. For this reason, explosive synchronization transitions, which facilitate fast, abrupt changes between these functional states, has recently seen significant interest from researchers. While previous work has identified properties of complex systems that support explosive synchronization, these investigations have been conducted largely on an ad hoc basis. Here we provide an exact criterion for explosive synchronization in coupled phase oscillator ensembles by investigating the necessary relationship between dynamical and structural disorder. This result provides a critical step towards untangling the intertwined properties of complex systems responsible for abrupt phase transitions and bistability in biological and engineered systems.

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Phys. Rev. Research 4, L032033– Published 22 August, 2022
  • Received 8 June 2022
  • Accepted 12 August 2022
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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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