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Stability of synchronization systems with inertia against frequency perturbations
Jiachen Ye1, Peng Ji2, Vinko Zlatić3
1School of Mathematics, Physics and Statistics, Shanghai Polytechnic University, 201209 Shanghai, China.
Chaos (Woodbury, N.Y.)
|October 23, 2025
Summary
We studied the stability of the Kuramoto model with inertia against frequency perturbations. Network structure and parameters jointly influence stability, with rapid vibration potentially counteracting stability loss.
Area of Science:
- Complex systems
- Network science
- Theoretical physics
Background:
- Synchronization is crucial for systems like power grids.
- The Kuramoto model is a key theoretical tool for studying synchronization.
- Adding inertia to the Kuramoto model enhances realism but increases complexity.
Purpose of the Study:
- Investigate the stability of the inertia-enhanced Kuramoto model.
- Analyze the impact of frequency perturbations on system stability.
- Quantify the interplay between network properties and stability.
Main Methods:
- Utilized the Kuramoto model with an inertia term.
- Employed the fragility performance metric to assess stability.
- Analyzed the influence of dynamical parameters and network spectral characteristics.
Main Results:
- Revealed how dynamical parameters and network spectral characteristics jointly affect stability.
- Demonstrated intrinsic differences in stability based on network structures.
- Identified the 'rapid vibration effect' where rapid perturbations can counteract stability loss.
Conclusions:
- System stability is a complex interplay of network topology and dynamics.
- The inertia term in the Kuramoto model offers a more realistic yet analytically challenging framework.
- Understanding perturbation effects is key to ensuring the stability of synchronized systems.
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