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Bifurcations in the Kuramoto model with external forcing and higher-order interactions
Guilherme S Costa1, Marcel Novaes2,3, Marcus A M de Aguiar1,3
1ICTP South American Institute for Fundamental Research & Instituto de Física Teórica-UNESP, São Paulo, SP 01140-070, Brazil.
Chaos (Woodbury, N.Y.)
|December 5, 2024
Summary
We explored the Kuramoto model with external forcing and higher-order interactions, revealing 11 distinct system states. This combination creates complex synchronization dynamics, impacting both forced and spontaneous behaviors.
Area of Science:
- Complex systems science
- Nonlinear dynamics
- Theoretical physics
Background:
- Synchronization is crucial in natural and artificial systems, from neurons to power grids.
- The Kuramoto model is a fundamental tool for studying synchronization phenomena.
- Real-world systems often exhibit external periodic forcing and higher-order interactions.
Purpose of the Study:
- To investigate the Kuramoto model with combined external periodic forcing and higher-order interactions.
- To analyze the resulting complex bifurcation scenarios and emergent system states.
- To understand the interplay between forced and spontaneous synchronization.
Main Methods:
- Mathematical analysis of the Kuramoto model.
- Exploration of parameter space for bifurcation analysis.
- Identification and characterization of asymptotic states.
Main Results:
- The combined forcing and higher-order interactions yield a rich bifurcation scenario.
- Eleven distinct asymptotic states were identified in the system.
- Competition between externally forced and spontaneous synchronization was observed.
- Saddle-node, Hopf, and homoclinic manifolds were found to be duplicated in bi-stable regions.
Conclusions:
- The interplay of external forcing and higher-order interactions significantly enriches the dynamics of the Kuramoto model.
- This combined approach leads to complex synchronization behaviors and multiple stable states.
- The findings provide insights into the diverse synchronization patterns observed in complex systems.
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