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Type: Journal article
Title: Control of Weierstrass–Mandelbrot function model with Morlet wavelets
Author: Zhang, L.
Liu, S.
Yu, C.
Citation: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2014; 24(10):1450121-1-1450121-9
Publisher: World Scientific
Issue Date: 2014
ISSN: 0218-1274
Statement of
Li Zhang, Shutang Liu, Chenglong Yu
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.
Keywords: Control; Weierstrass–Mandelbrot function; Morlet wavelet; multifractality; Hurst exponent
Rights: © World Scientific Publishing Company
DOI: 10.1142/S0218127414501211
Appears in Collections:Aurora harvest 3
Mathematical Sciences publications

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