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Related Experiment Videos

Destabilization patterns in chains of coupled oscillators.

Serhiy Yanchuk1, Matthias Wolfrum

  • 1Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 21, 2008
PubMed
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We reveal how coupled oscillators destabilize, leading to complex network behaviors like multiple coexisting periodic orbits. This phenomenon occurs even with unidirectional coupling, challenging existing models.

Area of Science:

  • Nonlinear Dynamics
  • Complex Systems
  • Network Science

Background:

  • Coupled oscillators exhibit rich dynamical behaviors.
  • Understanding network destabilization is crucial for complex systems.
  • Existing models often assume bidirectional or spatial coupling.

Purpose of the Study:

  • To elucidate the mechanism of destabilization in a chain of identical coupled oscillators.
  • To characterize the complex bifurcation scenario in such networks.
  • To investigate the role of unidirectional coupling in network dynamics.

Main Methods:

  • Analysis of stationary to oscillatory transitions in single oscillators.
  • Investigation of bifurcation scenarios in coupled oscillator networks.
  • Examination of spectral problems and limiting equations for large networks.

Related Experiment Videos

  • Study of purely convective unidirectional coupling effects.

    • Main Results:

    • Identified a complex bifurcation scenario with coexisting multiple periodic orbits.
    • Observed different frequencies, spatial patterns, and modulation instabilities.
    • Demonstrated this scenario occurs with purely convective unidirectional coupling.
    • Showed the phenomenon is not a simple discretization of continuous systems.

    Conclusions:

    • The destabilization mechanism involves a complex bifurcation scenario.
    • Unidirectional coupling can lead to intricate network dynamics previously unexplained.
    • The analysis is independent of network size by using limiting equations.