Harikrishnan, K. P. ; Misra, R. ; Ambika, G. ; Amritkar, R. E. (2010) Parametric characterisation of a chaotic attractor using the two scale cantor measure Physica D: Nonlinear Phenomena, 239 (8). pp. 420-427. ISSN 0167-2789
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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S01672...
Related URL: http://dx.doi.org/10.1016/j.physd.2010.01.008
Abstract
A chaotic attractor is usually characterised by its multifractal spectrum which gives a geometric measure of its complexity. Here we present a characterisation using a minimal set of independent parameters which is uniquely determined by the underlying process that generates the attractor. The method maps the f(α ) spectrum of a chaotic attractor on to that of a general two scale Cantor measure. We show that the mapping can be done in practice with reasonable accuracy for many of the standard chaotic attractors. In order to implement this procedure, we also propose a generalisation of the standard equations for the two scale Cantor set in one dimension to that in higher dimensions. Another interesting result we have obtained both theoretically and numerically is that, the f(α ) characterisation gives information only up to two scales, even when the underlying process generating the multifractal involves more than two scales.
Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |
Keywords: | Chaotic Attractor; Multifractal Spectrum; Cantor Set |
ID Code: | 510 |
Deposited On: | 21 Sep 2010 10:38 |
Last Modified: | 16 May 2016 11:43 |
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