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Related Experiment Videos

Large deviation properties of on-off intermittency.

H Suetani1, T Horita

  • 1Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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This study explores on-off intermittency using a two-dimensional map. Researchers found a second-order phase transition in burst state behavior, linked to the intermittency

Area of Science:

  • Nonlinear Dynamics
  • Statistical Physics
  • Chaos Theory

Background:

  • On-off intermittency is a phenomenon observed in dynamical systems characterized by intermittent bursts of activity.
  • Understanding the statistical properties of these bursts is crucial for characterizing chaotic behavior.
  • Large deviation theory provides a framework for analyzing rare events in stochastic processes.

Purpose of the Study:

  • To investigate the large deviation properties of on-off intermittency.
  • To analyze the statistical behavior of the burst state in a piecewise linear map model.
  • To identify phase transitions associated with the onset of on-off intermittency.

Main Methods:

  • Introduction of a two-dimensional piecewise linear map.
  • Mapping the system to an infinite Markov chain.

Related Experiment Videos

  • Analysis of the q-weighted average of time spent in the burst state.

    • Main Results:

    • A nonanalyticity was observed in the q-weighted average of the burst state duration.
    • This nonanalyticity manifests as a second-order phase transition.
    • The transition occurs over an interval of the control parameter, ending at the bifurcation point of on-off intermittency.

    Conclusions:

    • The study successfully links large deviation properties of on-off intermittency to phase transitions.
    • The piecewise linear map serves as a valuable model for understanding complex intermittent dynamics.
    • The findings provide insights into the critical behavior at the onset of chaos.