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Frequency dispersion in the time-delayed Kuramoto model.

Anders Nordenfelt1, Alexandre Wagemakers1, Miguel A F Sanjuán1

  • 1Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.

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Time delays in Kuramoto oscillator networks with identical natural frequencies cause frequency dispersion in networks with varied connectivity. This deviation from natural frequency leads to intermediate states between synchronization and incoherence.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Network Science

Background:

  • Kuramoto oscillators are widely used to model synchronization in coupled systems.
  • Time delays are crucial in many real-world networks, affecting system dynamics.
  • Understanding frequency distribution is key to characterizing network states.

Purpose of the Study:

  • To investigate the effects of time delays on synchronization and frequency distribution in Kuramoto oscillator networks.
  • To analyze the role of degree distribution in emergent network phenomena.
  • To identify the mechanisms driving frequency dispersion.

Main Methods:

  • Simulations of time-delayed Kuramoto oscillator networks with identical natural frequencies.
  • Analysis of frequency distribution based on network degree heterogeneity.
  • Mathematical identification of frequency deviation contributions.

Main Results:

  • Pronounced frequency dispersion observed in networks with nonidentical degree distributions.
  • Time-delay-induced deviation of average network frequency from natural frequency is essential for dispersion.
  • Identified intermediate states between perfect synchronization and complete incoherence.

Conclusions:

  • Network degree distribution significantly impacts frequency dynamics in the presence of time delays.
  • The interplay between time delay and network structure generates complex emergent behaviors.
  • These findings offer insights into partially synchronized states in complex systems.