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Nature of the Volcano Transition in the Fully Disordered Kuramoto Model
Axel Prüser1, Sebastian Rosmej1, Andreas Engel1
1Carl von Ossietzky University Oldenburg, Institut für Physik, D26111 Oldenburg, Germany.
Physical Review Letters
|May 17, 2024
Summary
We analyzed the synchronization of randomly coupled phase oscillators, revealing a volcano transition. This transition is linked to the emergence of an oscillator glass phase in the Kuramoto model.
Area of Science:
- Physics
- Complex Systems
- Statistical Mechanics
Background:
- Randomly coupled phase oscillators can exhibit complex collective behaviors, including synchronization into disordered patterns.
- The Kuramoto model is a standard framework for studying synchronization phenomena in coupled oscillator systems.
Purpose of the Study:
- To analyze the transition to disordered collective motion in a large, fully connected Kuramoto model with random interactions.
- To clarify the nature of the 'volcano transition' and its relationship with an oscillator glass phase.
Main Methods:
- Utilized the dynamical cavity method to simplify the complex system dynamics.
- Reduced the many-oscillator problem to a tractable stochastic single-oscillator problem.
- Employed analytical and numerical studies of self-consistent correlation and response functions.
Main Results:
- Characterized the synchronization transition in the Kuramoto model with symmetric, independent random interactions.
- Identified and explained the mechanism behind the 'volcano transition'.
- Established a clear link between this transition and the formation of an oscillator glass phase.
Conclusions:
- The dynamical cavity method provides a powerful tool for understanding complex synchronization phenomena.
- The oscillator glass phase is a key feature associated with the volcano transition in randomly coupled oscillator systems.
- This study offers new insights into the statistical mechanics of disordered systems.
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