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This study explores phase-lag effects in coupled oscillator networks, revealing metastable dynamics and diverse spatiotemporal patterns. The findings offer insights into brain network synchronization.

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Area of Science:

  • Dynamical systems
  • Theoretical neuroscience
  • Complex systems

Background:

  • The Kuramoto-Sakaguchi model describes coupled oscillator synchronization.
  • Understanding collective dynamics in oscillator networks is crucial for various fields, including neuroscience.
  • The Ott-Antonsen ansatz simplifies analysis of large populations of coupled oscillators.

Purpose of the Study:

  • To investigate the influence of the phase-lag parameter (α) on the collective dynamics of an Ott-Antonsen reduced M-population of Kuramoto-Sakaguchi oscillators.
  • To characterize the range of spatiotemporal patterns and transitions between them.
  • To analyze the stability of different dynamic states and their dependence on the phase-lag parameter.

Main Methods:

  • Utilized the Ott-Antonsen reduced M-population model for Kuramoto-Sakaguchi oscillators.
  • Performed linear stability analysis to determine stable regions of coherent states.
  • Investigated spatiotemporal patterns and transitions for varying phase-lag parameters (α).

Main Results:

  • Observed diverse spatiotemporal patterns: coherent, traveling waves, partially synchronized, modulated, and incoherent states.
  • Identified back-and-forth transitions between states, indicating metastability.
  • Found stable traveling wave solutions in certain α ranges, even when coherent states were also stable.
  • Determined specific α ranges associated with frequent metastable transitions between different states (e.g., coherent and partially synchronized states around α≈0.46π).

Conclusions:

  • The phase-lag parameter significantly influences the collective dynamics and emergent patterns in oscillator networks.
  • Metastable dynamics, characterized by frequent transitions between states, are a key feature of this system.
  • The model provides a framework for understanding complex phenomena like brain network synchronization and metastability.