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Dual role of higher-order interactions in the stability of twisted states in high-harmonic Kuramoto-Sakaguchi models

Author

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  • Wang, Xueqin
  • Yu, Dong
  • Xie, Ying
  • Li, Xuening
  • Ye, Zhiqiu
  • Jia, Ya

Abstract

Despite extensive studies on multicoherent-phase structures induced by high-harmonic coupling, the role of higher-order interactions in shaping the stability of twisted states remains poorly understood. In this work, we introduce higher-order interactions into a discrete high-harmonic Kuramoto-Sakaguchi (KS) model and systematically investigate the stability properties of twisted states. We show that, for generic twisted states, increasing higher-order interactions and phase lag enhances their linear stability, whereas this stabilizing effect is weakened as the harmonic order increases. In contrast, for two-cluster twisted states with small twist numbers, higher-order interactions and phase lag significantly suppress stability and lead to a pronounced shrinkage of the basin of attraction of twisted states. However, increasing the coupling range tends to mitigate this basin-shrinking tendency. These findings uncover a dual role of higher-order interactions in multicoherent dynamics and provide new insights into the formation and stability of twisted states in complex coupled systems.

Suggested Citation

  • Wang, Xueqin & Yu, Dong & Xie, Ying & Li, Xuening & Ye, Zhiqiu & Jia, Ya, 2026. "Dual role of higher-order interactions in the stability of twisted states in high-harmonic Kuramoto-Sakaguchi models," Chaos, Solitons & Fractals, Elsevier, vol. 208(P3).
    • Handle: RePEc:eee:chsofr:v:208:y:2026:i:p3:s0960077926004042
    DOI: 10.1016/j.chaos.2026.118263
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