Control of weierstrass-mandelbrot function model with morlet wavelets

Li Zhang, Shutang Liu, Chenglong Yu

    Research output: Contribution to journalArticle

    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

    Keywords

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

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