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Synchronization in symmetric bipolar population networks.

Lubos Buzna1, Sergi Lozano, Albert Díaz-Guilera

  • 1ETH Zurich, UNO C 14, Universitätstrasse 41, Zurich, Switzerland. buzna@frdsa.uniza.sk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary

We studied Kuramoto oscillators with two frequency values, finding that synchronization improves when nodes with opposite frequencies interact. This research provides an analytical method to determine the coupling strength needed for global synchronization.

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Network science

Background:

  • Kuramoto oscillators are fundamental models for studying synchronization in coupled systems.
  • Real-world networks often exhibit heterogeneity, with nodes having distinct roles or properties, such as energy generation/consumption in power grids.

Purpose of the Study:

  • To investigate the synchronization dynamics of Kuramoto oscillators with a bimodal distribution of natural frequencies.
  • To explore the impact of topological localization of these frequencies on synchronization.
  • To derive an analytical estimation for the critical coupling strength required for global synchronization.

Main Methods:

  • Analysis of Kuramoto oscillator populations with two distinct natural frequencies.
  • Consideration of correlations between node frequency values and their positions within regular and random network topologies.
  • Development of an analytical estimation for the minimum coupling strength for global synchronization.

Main Results:

  • Synchronization is enhanced when nodes are adjacent to nodes with opposite frequencies.
  • An analytical estimation for the critical coupling strength was derived.
  • The analytical estimation shows strong agreement with numerical simulations.

Conclusions:

  • Topological localization of natural frequencies significantly influences synchronization dynamics in complex networks.
  • The derived analytical estimation offers a valuable tool for predicting and understanding synchronization thresholds.
  • This work deepens the understanding of synchronization in heterogeneous oscillator populations.