Frustrated Synchronization of the Kuramoto Model on Complex Networks
Géza Ódor1, Shengfeng Deng2, Jeffrey Kelling3,4
1Institute of Technical Physics and Materials Science, HUN-REN Centre for Energy Research, P.O. Box 49, H-1525 Budapest, Hungary.
Entropy (Basel, Switzerland)
|January 8, 2025
Summary
We studied synchronization transitions in the Kuramoto model on large networks. Network heterogeneity causes frustrated synchronization, differing from regular lattices.
Area of Science:
- Complex systems
- Network science
- Statistical physics
Background:
- The Kuramoto model is a standard framework for studying synchronization phenomena in coupled oscillator systems.
- Understanding synchronization transitions in large and complex networks is crucial for various scientific domains.
- Heterogeneous networks with long-range connections can exhibit distinct dynamical behaviors compared to regular lattices.
Purpose of the Study:
- To investigate the synchronization transition of the locally coupled Kuramoto model on extremely large regular lattices and heterogeneous networks with power-law decaying long links.
- To compare the critical behavior and scaling properties of synchronization in these different network structures.
- To elucidate the role of network heterogeneity in synchronization dynamics.
Main Methods:
- Simulations of the Kuramoto model on large regular lattices (405x405 and 1004x1004) and heterogeneous networks (12,000x12,000) with power-law decaying long links.
- Analysis of synchronization transition using concepts of spectral dimensions (ds) and corrections to scaling.
- Comparison of mean-field and non-mean-field critical behaviors.
Main Results:
- Regular lattices show mean-field criticality with logarithmic corrections at d=4 and strong corrections at d=5 spectral dimensions.
- Heterogeneous networks with long links exhibit a non-mean-field smeared transition with oscillating corrections at high spectral dimensions (ds>4).
- Network heterogeneity significantly alters synchronization dynamics, leading to frustrated synchronization.
Conclusions:
- The heterogeneity of networks with long links is a crucial factor influencing synchronization transitions.
- The observed frustrated synchronization in heterogeneous networks resembles Griffiths effects.
- This study highlights the importance of network topology in determining collective dynamics and phase transitions.
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