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Noise stability of synchronization and optimal network structures.

Yuriko Katoh1, Hiroshi Kori2

  • 1NTT DATA Mathematical Systems Inc., Tokyo 160-0016, Japan.

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Summary

This study introduces a framework to measure synchronization in noisy oscillator networks. It helps identify optimal network structures and oscillator placements for improved synchronization.

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Area of Science:

  • Complex Systems
  • Network Science
  • Nonlinear Dynamics

Background:

  • Synchronization is a fundamental phenomenon in many natural and engineered systems.
  • Understanding factors influencing synchronization in networks of noisy oscillators is crucial.
  • Quantifying individual node and link contributions to synchronization remains a challenge.

Purpose of the Study:

  • To develop a theoretical framework for quantifying expected synchronization levels in noisy oscillator networks.
  • To identify key network properties and oscillator characteristics that impact synchronization.
  • To provide methods for optimizing network structure and oscillator configuration for enhanced synchronization.

Main Methods:

  • Linearization of the synchronized state for analysis of multivariate Ornstein-Uhlenbeck processes.
  • Derivation of fluctuation magnitudes and disturbance coefficients from network Laplacian eigenvalues and eigenfunctions.
  • Application of the theoretical framework to various example networks.

Main Results:

  • A method to quantify the impact of individual nodes and links on network synchronization.
  • Identification of disturbance coefficients (αᵢ) indicating how strongly each node affects synchronization.
  • The framework successfully elucidates optimal network structures and oscillator configurations for heterogeneous noise levels.

Conclusions:

  • The developed theoretical framework provides a quantitative approach to understanding and optimizing synchronization in complex networks.
  • This work offers practical insights for designing networks with desired synchronization properties.
  • The findings are applicable to diverse fields relying on synchronized oscillatory behavior.