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We developed a new framework to compare how coupled oscillators synchronize across networks. This method quantizes synchronization differences, aiding the analysis of complex system dynamics and network structures.

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Area of Science:

  • Complex Systems
  • Network Science
  • Dynamical Processes

Background:

  • Synchronization is crucial in many complex systems, from biological networks to power grids.
  • Understanding how network structure influences synchronization dynamics is a key challenge.

Purpose of the Study:

  • To introduce a general framework for comparing synchronization dynamics in coupled oscillator systems.
  • To quantify dissimilarities between synchronization processes on networks of identical size.

Main Methods:

  • Developed a dissimilarity measure based on a hypertorus metric for comparing oscillator phases.
  • Applied the framework to the Kuramoto model with various network configurations (e.g., edge weights, cycles, rings).
  • Compared synchronization in nonisomorphic graphs and contrasted the Kuramoto model with its linear approximation.

Main Results:

  • Analyzed the impact of network topology and coupling parameters on oscillator synchronization.
  • Quantified synchronization differences for various network structures and initial conditions.
  • Demonstrated the framework's utility in comparing different dynamical models.

Conclusions:

  • The proposed framework offers a versatile tool for analyzing and comparing synchronization phenomena in complex networks.
  • It facilitates a deeper understanding of how network structure dictates system dynamics.
  • The method is applicable to diverse systems exhibiting coupled oscillator behavior.