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Long chaotic transients in complex networks.

Alexander Zumdieck1, Marc Timme, Theo Geisel

  • 1Max-Planck-Institut für Strömungsforschung and Fakultät für Physik, Universität Göttingen, 37073 Göttingen, Germany.

Physical Review Letters
|February 9, 2005
PubMed
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Long chaotic transients, not rapid convergence, dominate randomly diluted pulse-coupled oscillator networks. Transient lengths depend heavily on connectivity, peaking at intermediate levels, and exhibit novel synchronization.

Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Network science

Background:

  • Networks of pulse-coupled oscillators are fundamental in various scientific fields.
  • Globally coupled networks typically exhibit rapid convergence to stable states.
  • The dynamics of randomly diluted networks remain less understood.

Purpose of the Study:

  • To investigate the dominant dynamics in randomly diluted networks of pulse-coupled oscillators.
  • To characterize the nature and dependencies of transient behavior.
  • To explore synchronization phenomena within these transient dynamics.

Main Methods:

  • Analysis of chaotic transients in randomly diluted networks.
  • Investigation of the dependence of transient lengths on network connectivity.

Related Experiment Videos

  • Calculation of an approximation for the largest Lyapunov exponent.

    • Main Results:

    • Long chaotic transients, rather than rapid convergence, characterize the dynamics.
    • Transient lengths vary significantly (orders of magnitude) with network connectivity.
    • Maximum transient lengths are observed at intermediate connectivities.
    • A novel form of robust synchronization is identified within the transients.

    Conclusions:

    • Chaotic transients are a key feature of randomly diluted oscillator networks.
    • Network connectivity critically influences transient duration and dynamics.
    • The findings offer new insights into synchronization in complex networks.