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Emergence of antiphase synchronous states in small-size systems with 2-simplex coupling

Author

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  • Wang, Xuan
  • Li, Haihong
  • Li, Yang
  • Cheng, Haoxin
  • Dai, Qionglin
  • Yang, Junzhong

Abstract

This study investigates the emergence of antiphase fully synchronous states (AFSs) in small-size systems with 1-simplex and 2-simplex interactions. We focus on the influence of system size (N) on the existence of AFSs and reveal that the interplay between the second-harmonic and three-body coupling terms within the 2-simplex, in conjunction with N, significantly impacts the formation of AFSs. Our analysis elucidates that under thermodynamic limits (N→∞), in-phase synchronous state are exclusive. It also reveals that second-harmonic coupling promotes the emergence of AFSs. However, as the number of oscillators N increases, the facilitative effect of second-harmonic coupling on AFSs is diminished, leading to a predominance of IFS over AFSs. We determine the upper limit of N above which AFSs cannot be observed in the 2-simplex system. This research bridges the dynamics from small-size systems to the thermodynamic limit, offering insights into the complex synchronization phenomena in networks of interconnected phase oscillators of higher-order interaction.

Suggested Citation

  • Wang, Xuan & Li, Haihong & Li, Yang & Cheng, Haoxin & Dai, Qionglin & Yang, Junzhong, 2025. "Emergence of antiphase synchronous states in small-size systems with 2-simplex coupling," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:chsofr:v:196:y:2025:i:c:s0960077925003327
    DOI: 10.1016/j.chaos.2025.116319
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