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

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

Chaos, Solitons & Fractals, 2025, vol. 196, issue C

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.

Keywords: Synchronization; Coupled oscillators; High-order interactions; Phase transition (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:196:y:2025:i:c:s0960077925003327

DOI: 10.1016/j.chaos.2025.116319

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