Control of weierstrass-mandelbrot function model with morlet wavelets

Li Zhang, Shutang Liu, Chenglong Yu

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1 Citation (Scopus)

Abstract

A Weierstrass-Mandelbrot function (WMF) model with Morlet wavelets is investigated. Its control relationships are derived quantitatively after proving the convergence of the controlled WMF model. Based on these relationships, it is shown that the scope of the WMF series increases with three parameters of the Morlet wavelets. But other parameters have opposite effect on the scope of the series. The results of simulated examples demonstrate the effectiveness of the control method. Moreover, two statistical characteristics of the series are obtained as the parameters change: One is multifractality of the series of the controlled WMF model, and the other is the Hurst exponent whose value stands for the long-time memory effect on the series.

Original languageEnglish
Article number1450121
Number of pages9
JournalInternational Journal of Bifurcation and Chaos
Volume24
Issue number10
DOIs
Publication statusPublished - 8 Nov 2014
Externally publishedYes

Keywords

  • Control
  • Hurst exponent
  • Morlet wavelet
  • Multifractality
  • Weierstrass-Mandelbrot function

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