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Related Experiment Videos

Unstable attractors induce perpetual synchronization and desynchronization.

Marc Timme1, Fred Wolf, Theo Geisel

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

Chaos (Woodbury, N.Y.)
|April 5, 2003
PubMed
Summary

Contrary to intuition, unstable attractors naturally arise in pulse-coupled oscillator networks. Weak noise induces switching between synchronized and desynchronized states, dominating network dynamics.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Network science

Background:

  • Invariant sets in nonlinear dynamical systems are typically assumed to be stable.
  • Intuition suggests that attracting sets should be stable, guiding system behavior predictably.

Purpose of the Study:

  • To investigate the emergence and role of unstable attractors in a network of pulse-coupled oscillators.
  • To challenge the common assumption of stability for attracting sets in dynamical systems.

Main Methods:

  • Modeling a network of pulse-coupled oscillators.
  • Analyzing system dynamics from random initial conditions.
  • Investigating the influence of noise on synchronization and desynchronization phenomena.

Main Results:

Related Experiment Videos

  • Unstable attractors arise naturally in the pulse-coupled oscillator network.
  • Weak noise induces a switching phenomenon between synchronized clusters and desynchronized states.
  • These unstable attractors dominate the network dynamics, especially for large networks and broad parameter ranges.

Conclusions:

  • The study demonstrates the natural occurrence and dominance of unstable attractors in complex dynamical systems.
  • The findings challenge conventional understanding of attractor stability in nonlinear systems.
  • The observed switching dynamics highlight the complex behavior arising from unstable attractors in networked systems.