Quick estimation of escape rate with the help of fractal dimension

  • Csernák G
  • Stépán G
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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. © 2005 Elsevier B.V. All rights reserved.

Author-supplied keywords

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

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Authors

  • Gábor Csernák

  • Gábor Stépán

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