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Updated: Jan 19, 2026
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AC Synchronous Machine; Prime-Mover Initialization
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Synchronization in starlike networks of phase oscillators
Can Xu1, Jian Gao2, Stefano Boccaletti3,4
1Institute of Systems Science and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China.
Physical Review. E
|September 11, 2019
Summary
This study analytically determines synchronization routes and phase transition critical points in starlike networks of phase oscillators. It reveals invariant relaxation rates, offering new insights into complex network dynamics.
Area of Science:
- Physics
- Network Science
- Nonlinear Dynamics
Background:
- Synchronization is crucial in coupled oscillator systems.
- Starlike networks are fundamental in technological and biological systems.
- Classical Kuramoto theory provides a baseline for understanding synchronization.
Purpose of the Study:
- To analytically describe synchronization mechanisms in starlike networks.
- To determine routes to synchronization and critical points for phase transitions.
- To extend synchronization theory beyond classical models.
Main Methods:
- Analytical determination of synchronization routes.
- Application of singular perturbation theory.
- Analysis of quasi-Hamiltonian properties arising from network symmetry.
Main Results:
- Identified specific mechanisms and critical points for synchronization.
- Unveiled invariant relaxation rates to equilibrium states.
- Demonstrated a quasi-Hamiltonian property due to coupling symmetry.
Conclusions:
- The findings provide a deeper understanding of synchronization in starlike networks.
- The results are applicable to real-world technological and biological networks.
- This work offers a new perspective on phase transitions in complex systems.
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