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Erratum: "Effects of synaptic and myelin plasticity on learning in a network of Kuramoto phase oscillators" [Chaos 29, 083122 (2019)].

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Time-delayed Kuramoto model in the Watts-Strogatz small-world networks.

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Area of Science:

  • Complex systems
  • Network science
  • Nonlinear dynamics

Background:

  • Phase oscillators are fundamental in modeling coupled systems.
  • Small-world networks exhibit unique topological properties.
  • Time delays significantly impact network dynamics and synchronization.

Purpose of the Study:

  • To investigate the effect of uniform time delay on the synchronization of identical coupled phase oscillators in small-world networks.
  • To characterize the transitions between different dynamical states, including partially synchronized and glassy phases.
  • To identify indicators of discontinuous transitions and explore the emergence of Chimera states.

Main Methods:

  • Simulations of Kuramoto phase oscillators on small-world networks.
  • Systematic variation of intrinsic frequency, coupling constant, and time delay.
  • Analysis of frequency distributions, phase-locking patterns, and order parameters.
  • Identification of hysteresis loops and Chimera states.

Main Results:

  • Synchronization enhancement observed within specific time delay ranges.
  • Discontinuous transitions identified between partially synchronized states and a glassy phase.
  • Bimodal frequency distributions and hysteresis loops confirm discontinuous transitions.
  • Chimera states observed at the onset of these transitions.

Conclusions:

  • Time delay is a critical parameter controlling synchronization in small-world oscillator networks.
  • Discontinuous transitions and complex phenomena like Chimera states emerge due to time delays.
  • The findings provide insights into the rich dynamics of delayed complex networks.