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Mean field phase synchronization between chimera states.

Ralph G Andrzejak1, Giulia Ruzzene1, Irene Malvestio1

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Two coupled layers of phase oscillators can synchronize their mean fields, even when individual oscillators remain unsynchronized. This synchronization requires stronger coupling when network properties differ significantly.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Network Science

Background:

  • Phase oscillators are fundamental units in modeling coupled systems.
  • Chimera states, a mix of synchronized and desynchronized behavior, occur in networks.
  • Inter-layer coupling can induce novel synchronization phenomena.

Purpose of the Study:

  • Investigate synchronization in two-layer networks of phase oscillators.
  • Analyze the effect of mean-field coupling between layers.
  • Determine conditions for phase synchronization of network mean fields.

Main Methods:

  • Simulated two-layer ring networks of non-locally coupled phase oscillators.
  • Introduced bidirectional mean-field coupling between layers.
  • Varied network sizes, natural frequencies, and inter-layer coupling strength.

Main Results:

  • Achieved phase synchronization of mean fields across layers despite individual oscillator desynchronization.
  • Chimera states persisted within each layer.
  • Synchronization strength increased with mismatches in network size and natural frequencies.

Conclusions:

  • Mean-field phase synchronization is achievable in complex network systems.
  • This phenomenon is robust to heterogeneity within layers.
  • The findings offer insights into emergent synchronization in coupled dynamical systems.