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Information geometry and synchronization phase transition in the Kuramoto model.
Artem Alexandrov1, Alexander Gorsky2
1Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia and Laboratory of Complex Networks, Brain and Consciousness Research Center, Moscow, Russia.
Information geometry reveals synchronization transitions in the Kuramoto model. The Fisher information metric components diverge at critical points, offering new insights into collective dynamics.
Area of Science:
- Complex systems
- Statistical physics
- Information geometry
Background:
- The Kuramoto model is a widely used mathematical model for studying synchronization phenomena in systems of coupled oscillators.
- Understanding the transition to synchronized behavior is crucial for various scientific disciplines.
Purpose of the Study:
- To explore the application of information geometry to analyze the synchronization transition in the Kuramoto model.
- To identify sensitive measures within information geometry that capture critical phenomena.
Main Methods:
- Utilizing the framework of information geometry to analyze the Kuramoto model.
- Investigating the behavior of the Fisher information metric near the synchronization critical point.
- Connecting the Kuramoto model dynamics to geodesics in hyperbolic space.
Main Results:
- The Fisher information metric is shown to be sensitive to the synchronization transition.
- Specific components of the Fisher metric were found to diverge at the critical point of synchronization.
- A novel connection between the Kuramoto model and hyperbolic geometry was established.
Conclusions:
- Information geometry provides a powerful lens for understanding synchronization phenomena.
- The divergence of Fisher information metric components serves as a robust indicator of critical transitions.
- The established link to hyperbolic space opens new avenues for theoretical analysis of coupled oscillator systems.
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