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Higher-order interactions induce anomalous transitions to synchrony.
Iván León1,2, Riccardo Muolo3, Shigefumi Hata4
1Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8550, Japan.
Chaos (Woodbury, N.Y.)
|January 9, 2024
Summary
Higher-order interactions in coupled phase oscillators cause unusual synchronization behaviors, including multiple stable states and novel transition pathways. These findings extend beyond the standard Kuramoto model, even with oscillator frequency variations.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Statistical physics
Background:
- Coupled nonlinear oscillators are fundamental in various scientific fields.
- The Kuramoto model is a standard for studying oscillator synchronization.
- Higher-order interactions and phase lags are often simplified or ignored.
Purpose of the Study:
- To analyze a minimal model of coupled phase oscillators with two- and three-body interactions, including permutation symmetry and phase lags.
- To investigate the impact of higher-order interactions on synchronization phenomena.
- To explore anomalous transitions to synchrony and associated dynamical regimes.
Main Methods:
- Phase reduction of weakly coupled nonlinear oscillators.
- Theoretical analysis of a simplified model with higher-order interactions.
- Construction of phase diagrams for dynamical regimes.
- Verification through direct numerical simulations.
Main Results:
- Higher-order interactions induce anomalous transitions to synchrony.
- Multistability of full synchronization, incoherent, and two-cluster states are observed.
- Transitions to synchrony occur via slow switching and clustering.
- Similar transition scenarios persist even with slight oscillator frequency heterogeneity.
Conclusions:
- The inclusion of higher-order interactions significantly alters synchronization dynamics compared to the conventional Kuramoto model.
- Anomalous synchronization phenomena, including multistability and novel transition pathways, are characteristic of systems with higher-order coupling.
- The model provides a framework for understanding complex synchronization behaviors in diverse systems, even under heterogeneity.
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