Control of Weierstrass–Mandelbrot function model with Morlet wavelets
Date
2014
Authors
Zhang, L.
Liu, S.
Yu, C.
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Journal article
Citation
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2014; 24(10):1450121-1-1450121-9
Statement of Responsibility
Li Zhang, Shutang Liu, Chenglong Yu
Conference Name
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.
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© World Scientific Publishing Company