Title of article :
Parametric characterisation of a chaotic attractor using the two scale Cantor measure
Author/Authors :
Harikrishnan، نويسنده , , K.P. and Misra، نويسنده , , R. and Ambika، نويسنده , , G. and Amritkar، نويسنده , , R.E.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2010
Pages :
8
From page :
420
To page :
427
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.
Keywords :
Chaotic attractor , Multifractal spectrum , Cantor set
Journal title :
Physica D Nonlinear Phenomena
Serial Year :
2010
Journal title :
Physica D Nonlinear Phenomena
Record number :
1729316
Link To Document :
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