Life expectancy of transient microchaotic behaviour

G. Csernák, G. Stépán

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

The application of digital control may lead to so-called transient chaotic behaviour. In the present paper, we analyse a simple model of a digitally controlled mechanical system, which may create such vibrations. As a consequence of the digital effects, i.e., the sampling and the round-off error, the behaviour of this system can be described by a one-dimensional piecewise linear map. The lifetime of chaotic transients is usually characterized by the so-called escape rate. In the literature, the reciprocal of the escape rate is considered to be the expected duration of the transient chaotic phenomenon. We claim that this approach is not always fruitful, and present a different way of calculating the mean lifetime in the case of one-dimensional piecewise linear maps. Our method might also be used to solve diffusion problems in one-dimensional models of periodic arrays.

Original languageEnglish
Pages (from-to)63-91
Number of pages29
JournalJournal of Nonlinear Science
Volume15
Issue number2
DOIs
Publication statusPublished - Apr 1 2005

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)
  • Applied Mathematics

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