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The link between coherence echoes and mode locking.

Sebastian Eydam1, Matthias Wolfrum1

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Summary
This summary is machine-generated.

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.

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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.