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Rotating clusters in phase-lagged Kuramoto oscillators with higher-order interactions.

Bhuwan Moyal¹, Priyanka Rajwani¹, Subhasanket Dutta¹

¹Complex Systems Laboratory, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore-453552, India.

Physical Review. E

|April 18, 2024

Summary

This summary is machine-generated.

Higher-order interactions in phase-lagged Kuramoto oscillators shift synchronization critical points. Phase-lag controls cluster frequency, enabling new synchronization control methods.

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Area of Science:

Complex systems
Nonlinear dynamics
Network science

Background:

Pairwise interactions are well-studied in coupled oscillator systems.
Real-world systems exhibit complex, higher-order interactions beyond simple pairwise connections.
Phase-lag effects are crucial in synchronization phenomena.

Purpose of the Study:

Investigate the impact of higher-order interactions on phase-lagged coupled Kuramoto oscillators.
Determine how these interactions influence the transition from cluster synchronization to incoherence.
Explore the control of cluster synchronization frequency using phase-lag.

Main Methods:

Modeling coupled Kuramoto oscillators using simplicial complexes to represent higher-order interactions.
Analysis in polar coordinates to derive cluster rotation frequencies.
Application of the Ott-Antonsen approach in the thermodynamic limit.
Utilizing self-consistency methods to derive order parameters.

Main Results:

Higher-order interactions shift the critical point for the transition to incoherence.
Cluster rotation frequency is a function of the phase-lag parameter.
Phase-lag acts as a control parameter for cluster frequency.
A closed-form expression for the global synchronization order parameter was derived.

Conclusions:

Simplicial complex modeling reveals the significant role of higher-order interactions in phase-lagged oscillator synchronization.
Phase-lag offers a tunable parameter for controlling cluster synchronization dynamics.
The derived order parameter provides a more complete analytical description of global synchronization.