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The link between coherence echoes and mode locking
Sebastian Eydam1, Matthias Wolfrum1
1Weierstrass Institute for Applied Analysis and Stochastic, Mohrenstrasse 39, 10117 Berlin, Germany.
Chaos (Woodbury, N.Y.)
|November 3, 2019
Summary
This study reveals how self-organized mode locking in Kuramoto oscillator systems can generate sharp pulses. These findings explain coherence echoes and the impact of system parameters on collective dynamics.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Statistical physics
Background:
- Kuramoto oscillator systems exhibit collective dynamics, including synchronization and mode locking.
- Mode locking, characterized by periodic pulsations, has been observed below the synchronization threshold in systems with equidistant natural frequencies.
Purpose of the Study:
- To investigate the emergence of sharp pulses in the mean field of Kuramoto-type globally-coupled phase oscillator systems.
- To explore mode locking in systems with frequency combs of finite width and understand coherence echoes.
- To analyze the influence of interaction functions and external stimulations on these phenomena.
Main Methods:
- Analysis of Kuramoto-type globally-coupled phase oscillator systems.
- Investigating systems with equidistant natural frequencies and frequency combs with finite width.
- Studying the effects of system parameters, such as interaction functions and external stimulations.
Main Results:
- Mode locking, leading to sharp pulses, can occur in systems with frequency combs of finite width.
- Coherence echoes in disordered systems are explained by stimulation-induced mode locking of subpopulations.
- A second harmonic in the interaction function significantly enhances echo phenomena.
- Nonmonotonic echo amplitudes are linked to linear dispersion in mode-locked frequency combs.
- Global coupling supports stimulated pulsations in disordered systems by widening locking plateaus.
Conclusions:
- Sharp pulses in Kuramoto systems arise from self-organized mode locking, even with finite-width frequency combs.
- Coherence echoes are a manifestation of stimulation-induced mode locking.
- System parameters like interaction harmonics and external stimulations critically influence pulse generation and echo behavior.
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