On-off intermittency: Power spectrum and fractal properties of time series

Shankar C. Venkataramani, Thomas M. Antonsen, Edward Ott, John C. Sommerer

Research output: Contribution to journalArticle

115 Scopus citations

Abstract

Some dynamical systems possess invariant submanifolds such that the dynamics restricted to the invariant submanifold is chaotic. This situation arises in systems with a spatial symmetry or in the synchronization of chaotic oscillators. The invariant submanifold could become unstable to perturbations in the transverse directions when a parameter of the system is changed through a critical blow-out value. This could result in an extreme form of temporally intermittent bursting called on-off intermittency. We propose a model that incorporates the universal features of systems that display on-off intermittency. We study this model both with and without additive noise and we derive scaling results for the power spectral density of the on-off intermittent process and for the box counting dimension for the set of time intervals when the process takes on values above a given threshold. We then present numerical simulations realizing these results.

Original languageEnglish (US)
Pages (from-to)66-99
Number of pages34
JournalPhysica D: Nonlinear Phenomena
Volume96
Issue number1-4
DOIs
StatePublished - Jan 1 1996
Externally publishedYes

Keywords

  • Fractal dimension
  • Invariant manifold
  • On-off intermittency
  • Power spectrum
  • Universal scaling

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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