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