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Synchronization transitions in Kuramoto networks with higher-mode interaction.
Rico Berner1, Annie Lu2, Igor M Sokolov1
1Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany.
Chaos (Woodbury, N.Y.)
|July 18, 2023
Summary
This study explores synchronization in oscillator systems beyond the standard Kuramoto model. We found that two coupling modes create complex dynamics, leading to distinct oscillator groups.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Statistical physics
Background:
- Synchronization is a widespread phenomenon in nature and technology.
- Understanding real-world synchronization dynamics remains challenging.
- The Kuramoto model is a foundational but limited paradigm for studying synchronization.
Purpose of the Study:
- To investigate synchronization transitions in phase oscillator systems with two nonvanishing Fourier modes.
- To move beyond the limitations of the standard Kuramoto model.
- To elucidate the role of multiple coupling modes in synchronization dynamics.
Main Methods:
- Analysis of a phase oscillator system with a two-mode interaction function.
- Extension of the collective coordinate approach.
- Mathematical modeling of synchronization transitions.
Main Results:
- Synchronization scenarios are critically dependent on the interplay of two coupling modes.
- The presence of a second coupling mode induces multistability.
- The two-mode coupling leads to emergent states resembling two independent, interacting oscillator groups.
Conclusions:
- The two-mode coupling model offers a richer description of synchronization than the Kuramoto model.
- Emergent states can be characterized by independent yet interacting subgroups of oscillators.
- Findings encourage research into dynamical systems with complex interaction functions.
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