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Synchronization in asymmetrically coupled networks with node balance.

Igor Belykh1, Vladimir Belykh, Martin Hasler

  • 1Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA. ibelykh@mathstat.gsu.edu

Chaos (Woodbury, N.Y.)
|April 8, 2006
PubMed
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We found that asymmetrically connected oscillator networks can achieve global synchronization. This is possible if nodes have balanced input and output weights, matching results from symmetrized networks.

Area of Science:

  • Complex systems
  • Network science
  • Nonlinear dynamics

Background:

  • Synchronization is a fundamental phenomenon in coupled oscillator systems.
  • Understanding synchronization in complex networks is crucial for various scientific fields.
  • Asymmetric connections in networks present unique challenges for stability analysis.

Purpose of the Study:

  • To investigate the global stability of synchronization in asymmetrically connected oscillator networks.
  • To extend existing graph stability methods to directed networks with node balance.
  • To establish conditions for achieving synchronization bounds comparable to symmetrized networks.

Main Methods:

  • Extension of the connection graph stability method to directed graphs.
  • Analysis of networks exhibiting node balance (equal input and output weight sums).

Related Experiment Videos

  • Comparison of synchronization bounds between asymmetrically and symmetrized networks.

    • Main Results:

    • The study establishes an upper bound for synchronization in asymmetrically connected networks.
    • This upper bound is equivalent to that of a symmetrized network when node balance is satisfied.
    • The node balance condition is critical; without it, the property does not generally hold.

    Conclusions:

    • Global synchronization is achievable in asymmetrically connected oscillator networks under specific conditions.
    • Node balance is a key property that enables synchronization stability comparable to symmetrized systems.
    • The findings provide theoretical insights into the dynamics of complex networks with directed and unbalanced connections.