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Spatial patterns of desynchronization bursts in networks.

Juan G Restrepo1, Edward Ott, Brian R Hunt

  • 1Institute for Research in Electronics and Applied Physics and Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA. juanga@math.umd.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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We adapted the master stability function for networks of similar, not identical, chaotic oscillators. This revealed bubbling-induced desynchronization bursts with predictable spatial patterns, offering new insights into network dynamics.

Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Network Science

Background:

  • The master stability function (MSF) is crucial for analyzing synchronous states in identical chaotic oscillator networks.
  • Understanding network dynamics with non-identical oscillators presents significant challenges.

Purpose of the Study:

  • To adapt the MSF for networks of similar, non-identical chaotic oscillators.
  • To investigate the occurrence and characteristics of desynchronization bursts in such networks.

Main Methods:

  • Adaptation of the master stability function analysis.
  • Investigation of bubbling-induced desynchronization.
  • Analysis of spatial patterns using network connectivity and unstable periodic orbits.
  • Validation through numerical experiments.

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Main Results:

  • Identified bubbling-induced desynchronization bursts in networks of similar chaotic oscillators.
  • Demonstrated that burst spatial patterns are predictable from network topology and embedded unstable periodic orbits.
  • Characterized deviations from perfect synchrony when bursting is absent.

Conclusions:

  • The adapted MSF provides a powerful tool for analyzing complex dynamics in networks of non-identical oscillators.
  • Bubbling-induced bursts represent a key phenomenon in such networks, with predictable spatio-temporal characteristics.
  • Network structure and oscillator properties critically influence synchronous and desynchronous behaviors.