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Mode locking in systems of globally coupled phase oscillators
Sebastian Eydam1, Matthias Wolfrum1
1Weierstrass Institute for Applied Analysis and Stochastic, Mohrenstrasse 39, 10117 Berlin, Germany.
Physical Review. E
|January 20, 2018
Summary
Globally coupled phase oscillators exhibit stable sharp pulses in mean field amplitude, resembling laser mode locking. This phenomenon arises from nonlinear coupling and frequency spacing, leading to diverse dynamical regimes.
Area of Science:
- Physics
- Nonlinear Dynamics
- Complex Systems
Background:
- Kuramoto-type systems model synchronization in coupled oscillators.
- Understanding dynamics below the synchronization threshold is crucial for complex system behavior.
Purpose of the Study:
- Investigate dynamics in Kuramoto systems with equidistant frequencies below synchronization.
- Characterize the stable regime of sharp pulses and its relation to mode locking.
Main Methods:
- Analysis of globally coupled phase oscillators.
- Examination of nonlinear coupling effects on phase relations.
- Study of system size and harmonic contributions to stability.
Main Results:
- Observed stable sharp pulses in mean field amplitude with pulsation frequency tied to natural frequency spacing.
- Identified resemblance to laser mode locking due to nonlinear coupling-induced phase relations.
- Characterized bifurcating regimes: modulated mode locking, phase turbulence, intermittency, and type II supertransients.
Conclusions:
- Nonlinear coupling in Kuramoto systems can induce stable mode-locking-like behavior below synchronization.
- System dynamics exhibit rich bifurcations, including phase turbulence and supertransients.
- Harmonics play a key role in pulsation stability and emergent dynamics.
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