Synchronization transitions in adaptive Kuramoto-Sakaguchi oscillators with higher-order interactions
Abhishek Sharma1, Priyanka Rajwani1, Sarika Jalan1
1Complex Systems Lab, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India.
Chaos (Woodbury, N.Y.)
|August 30, 2024
Summary
This study explores coupled Kuramoto oscillators with phase lag and adaptation. Findings reveal how these factors alter synchronization transitions, offering insights into complex system dynamics.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Statistical Physics
Background:
- Coupled oscillator models are crucial for understanding synchronization in natural and artificial systems.
- The Kuramoto oscillator model is a fundamental framework for studying synchronization phenomena.
- Higher-order interactions and parameters like phase lag and adaptation introduce complexity to synchronization dynamics.
Purpose of the Study:
- To investigate the influence of phase lag and adaptation in higher-order interactions on the Kuramoto oscillator model.
- To analyze how these parameters affect the order of synchronization transitions.
- To explore the interplay between adaptation and phase lag in determining synchronization behavior.
Main Methods:
- Numerical simulations of the coupled Kuramoto oscillator model.
- Analysis of synchronization transitions (first-order, second-order, tiered synchronization).
- Application of the Ott-Antonsen approach for analytical descriptions in the thermodynamic limit.
Main Results:
- Synchronization transition order shifts from first-order to second-order, mediated by tiered synchronization, based on adaptation parameters.
- Phase lag facilitates these transitions at lower adaptation parameter exponents.
- The combined effect of adaptation and phase lag eliminates tiered synchronization, enabling a direct first-to-second-order transition.
Conclusions:
- Adaptation and phase lag are key parameters controlling synchronization transition types in higher-order coupled oscillator systems.
- The Ott-Antonsen approach provides accurate analytical predictions for synchronization dynamics, validated by numerical simulations.
- This research deepens the understanding of synchronization mechanisms in complex systems.
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