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Remote synchronization and critical-like breakdown in star networks of oscillator populations

Siyu Huo*

  • The Key Laboratory of Biomedical Information Engineering of Ministry of Education, Institute of Health and Rehabilitation Science, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China and Research Center for Brain-inspired Intelligence, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China

  • *Contact author: syhuo@xjtu.edu.cn
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Phys. Rev. Research 8, 043056 – Published 15 October, 2026

DOI: https://doi.org/10.1103/y4cy-9l8m

Abstract

Remote synchronization, in which indirectly connected nodes synchronize while the mediating hub remains desynchronized, is a counterintuitive form of collective dynamics in complex networks. Most previous studies have treated each node as a single oscillator, whereas nodes in realistic systems often represent populations of interacting dynamical units. Here, we study remote synchronization in a star network whose nodes are Kuramoto oscillator populations. Each node contains many internally coupled oscillators with coupling strength K, and different nodes interact through an internode coupling strength L. We show that remote synchronization emerges only at an intermediate level of internal synchrony: The leaf nodes become strongly synchronized with each other, while the hub remains weakly synchronized with them, when the internal order parameter is neither close to zero nor close to one. Increasing K further causes an abrupt breakdown of the remote-synchronized state. Detrended fluctuation analysis reveals enhanced scaling behavior and critical-like long-range temporal correlations near this breakdown boundary. A two-parameter scan in the (L,K) plane confirms that the remote-synchronized regime occupies a finite region associated with intermediate internal order and relatively low detrended fluctuation analysis exponent. We further provide a phenomenological effective-phase interpretation, showing that internal coupling controls the coherence, susceptibility, and stability of each oscillator population. These results demonstrate that internal population dynamics can regulate both the emergence and critical-like breakdown of remote synchronization.

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Phys. Rev. Research 8, 043056– Published 15 October, 2026
  • Received 15 July 2026
  • Accepted 7 October 2026
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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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