Quick estimation of escape rate with the help of fractal dimension

Gábor Csernák, Gábor Stépán

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The non-linearity caused by the application of digital control may lead to transient chaotic behaviour. In the present paper, we analyse a simple model of a digitally controlled mechanical system with dry friction, which may perform transient chaotic vibrations. As a consequence of the digital effects, the behaviour of this system can be described by a 1D piecewise linear map. The fractal dimension of the so-called chaotic repeller set is calculated and the results are used for the quick estimation of the mean lifetime of chaotic transients.

Original languageEnglish
Pages (from-to)595-605
Number of pages11
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume11
Issue number5
DOIs
Publication statusPublished - Aug 1 2006

Keywords

  • Digital control
  • Lifetime estimation
  • Multi-scale fractals
  • Transient chaos

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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