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One node driving synchronisation.

Chengwei Wang1, Celso Grebogi1, Murilo S Baptista1

  • 1Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen, AB24 3UE, UK.

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Summary
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A single critical node can trigger abrupt behavioral changes in complex networks. This study reveals network synchronization dynamics are governed by a key oscillator, independent of frequency distribution or network size.

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Area of Science:

  • Complex systems
  • Network dynamics
  • Nonlinear dynamics

Background:

  • Abrupt behavioral changes in complex networks can be initiated by individual nodes.
  • Understanding the influence of single nodes on network-wide behavior is crucial for predicting system dynamics.
  • Coupled phase-oscillator networks are fundamental models for studying synchronization phenomena.

Purpose of the Study:

  • To elucidate the dynamical principles governing how a single node's behavior impacts a heterogeneous network of coupled phase-oscillators.
  • To identify the critical factors determining network synchronization.
  • To develop novel analytical methods for calculating synchronization thresholds and phase-angles.

Main Methods:

  • Analysis of coupled phase-oscillator dynamics with heterogeneous coupling strengths.
  • Development of a novel method to compute the critical coupling strength for frequency synchronization.
  • Formulation of an analytical approach to approximate synchronous phase-angles.

Main Results:

  • Network synchronization is largely independent of natural frequency distribution and weakly dependent on network size.
  • Synchronization is critically determined by a single key oscillator with a maximum ratio of natural frequency to coupling strength.
  • A novel method for calculating critical coupling strength and an analytical method for phase-angle approximation were established.

Conclusions:

  • A single node's properties can dominantly influence the collective behavior and synchronization of complex networks.
  • The identified key oscillator provides a new perspective on network control and stability.
  • The developed analytical methods offer powerful tools for understanding and predicting synchronization in oscillator networks.