Quick estimation of escape rate with the help of fractal dimension

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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.

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Csernák, G., & Stépán, G. (2006). Quick estimation of escape rate with the help of fractal dimension. Communications in Nonlinear Science and Numerical Simulation, 11(5), 595–605. https://doi.org/10.1016/j.cnsns.2005.01.005

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