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  • Open Access

How interaction radius shapes vortex states in mobile phase oscillators

Jingtian Shang1,2, Yingshan Guo1,3, Zhigang Zheng1,4,*, and Changgui Gu5,†

  • *Contact author: zgzheng@hqu.edu.cn
  • †Contact author: gu_changgui@163.com
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Phys. Rev. Research 8, 043126 – Published 4 November, 2026

DOI: https://doi.org/10.1103/mzgk-nx4w

Abstract

Vortex patterns are a prominent form of collective organization in chiral active matter, yet how local interactions affect their persistence and eventual breakdown has not been fully clarified. We investigate vortex states in the Vicsek-Kuramoto model with different interaction ranges. For locally interacting mobile phase oscillators, vortex states persist over finite intervals of the coupling strength and are eventually replaced by the polar ordered state as the coupling strength increases. Adiabatic scans of the coupling strength reveal the coexistence of vortex and polar ordered states and lead to pronounced hysteresis, indicating that vortex states act as stable dynamical attractors rather than transient structures. To understand these behaviors, we combine continuum theory with linear stability analysis and show that the incoherent state first becomes unstable through the zero-wave-number mode, with a critical coupling strength identical to that of the classical Kuramoto model. By deriving the critical coupling strengths for the homogeneous mode and finite-wave-number modes, we demonstrate how the interaction range controls the separation of instability thresholds. These results characterize the dependence of collective states on the interaction radius and quantify its influence on the linear instability conditions of the incoherent state in the Vicsek-Kuramoto model.

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Phys. Rev. Research 8, 043126– Published 4 November, 2026
  • Received 6 June 2026
  • Accepted 16 October 2026
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