Transition to synchronization in the adaptive Sakaguchi-Kuramoto model with higher-order interactions
Sangita Dutta1, Prosenjit Kundu2, Pitambar Khanra3,4
1National Institute of Technology, Department of Mathematics, Durgapur 713209, India.
Physical Review. E
|February 7, 2025
Summary
We studied synchronization transitions in the Sakaguchi-Kuramoto model with higher-order interactions. We found continuous and discontinuous transitions, including explosive and tiered synchronization, using simulations and a reduced model.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Statistical physics
Background:
- The Sakaguchi-Kuramoto model is a fundamental framework for studying synchronization phenomena in coupled oscillator systems.
- Understanding transition dynamics is crucial for characterizing emergent collective behavior in diverse systems.
Purpose of the Study:
- To investigate the transition to synchronization in the Sakaguchi-Kuramoto model with higher-order interactions and global order parameter adaptation.
- To characterize different types of synchronization transitions, including continuous and discontinuous ones.
Main Methods:
- Extensive numerical simulations of the full Sakaguchi-Kuramoto system.
- Derivation and analysis of a reduced-order model (ROM) using the Ott-Antonsen ansatz.
- Analytical stability analysis of synchronization states.
Main Results:
- Numerical simulations revealed both continuous (second-order) and discontinuous transitions (first-order and tiered synchronization).
- The reduced-order model accurately reproduced the simulation results, providing deeper insights into parameter-dependent transition scenarios.
- Different transition types were linked to specific bifurcations: second-order to supercritical pitchfork bifurcation (PB), tiered to multiple saddle-node (SN) bifurcations and supercritical PB, and first-order to subcritical PB and SN bifurcation.
Conclusions:
- The study successfully characterized diverse synchronization transition scenarios in the Sakaguchi-Kuramoto model with higher-order interactions.
- The reduced-order model serves as a powerful analytical tool for understanding complex synchronization dynamics.
- The identified bifurcation mechanisms provide a fundamental understanding of emergent synchronization patterns.
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