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Synchronization in network geometries with finite spectral dimension.
Ana P Millán1, Joaquín J Torres, Ginestra Bianconi2
1Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain.
Network spectral dimension is key to understanding network dynamics. A spectral dimension above four ensures stable synchronization, while above two allows phase entrainment in oscillator networks.
Area of Science:
- Network science
- Complex systems
- Mathematical physics
Background:
- Growing interest in network geometry and topology.
- Understanding the relationship between network structure and dynamics is crucial.
Purpose of the Study:
- To investigate the role of spectral dimension in network dynamics.
- To establish a link between topological, geometrical, and dynamical properties of networks.
- To analyze the synchronization properties of the Kuramoto model in relation to spectral dimension.
Main Methods:
- Analytical derivation of the role of spectral dimension.
- Numerical simulations using the Kuramoto model.
- Testing predictions on complex network manifolds with tunable spectral dimension.
Main Results:
- Thermodynamically stable synchronized phase requires spectral dimensions > 4.
- Phase entrainment of oscillators is observed for spectral dimensions > 2.
- Analytical predictions validated on complex network manifolds.
Conclusions:
- Spectral dimension is a fundamental network property governing dynamics.
- The Kuramoto model's synchronization behavior is critically dependent on spectral dimension.
- Complex network manifolds provide a platform to study spectral dimension effects.
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