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Explosive synchronization in weighted complex networks.

I Leyva1, I Sendiña-Nadal, J A Almendral

  • 1Complex Systems Group, Univ. Rey Juan Carlos, 28933 Móstoles, Madrid, Spain and Center for Biomedical Technology, Univ. Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain.

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Summary
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Researchers developed a practical method to induce explosive synchronization in networked oscillators by combining local and global network information. This technique enhances control over system transitions and hysteresis.

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Area of Science:

  • Complex Systems
  • Network Science
  • Nonlinear Dynamics

Background:

  • Dynamical abrupt transitions in macroscopic systems are of significant interest.
  • Understanding synchronization in complex networks is crucial for various scientific fields.

Purpose of the Study:

  • To develop a practical weighting procedure to induce and enhance explosive, irreversible transitions to synchronization in phase oscillator networks.
  • To investigate the control over hysteresis in synchronization transitions.

Main Methods:

  • Combining dynamical local information on frequency mismatches with global graph topology.
  • Utilizing a judicious and practical weighting procedure.
  • Conducting extensive numerical and analytical investigations.

Main Results:

  • The proposed weighting procedure effectively induces and enhances explosive synchronization.
  • The method is valid and scalable across different frequency distributions and network types (homogeneous/heterogeneous).
  • Both linear and nonlinear weighting functions were successful.
  • Parametric control over the width and extent of the hysteretic region was achieved.

Conclusions:

  • A novel and effective method for controlling explosive synchronization in complex networks has been demonstrated.
  • The findings offer new possibilities for managing and controlling collective behaviors in networked systems.
  • The procedure's scalability and adaptability suggest broad applicability in diverse synchronization phenomena.