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Identification of Chaos-Periodic Transitions, Band Merging, and Internal Crisis Using Wavelet-Dfa Method Publisher



Vaghefi M1 ; Nasrabadi AM2 ; Golpayegani SMRH3 ; Mohammadi MR4 ; Gharibzadeh S3
Authors
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Authors Affiliations
  1. 1. Department of Biomedical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
  2. 2. Department of Biomedical Engineering, Faculty of Engineering, Shahed University, Tehran, Iran
  3. 3. Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, Iran
  4. 4. Psychiatry and Psychology Research Center, Roozbeh Hospital, Tehran University, of Medical Sciences, Tehran, Iran

Source: International Journal of Bifurcation and Chaos Published:2016


Abstract

Detrended Fluctuation Analysis (DFA) is a scaling analysis method that can identify intrinsic self-similarity in any nonstationary time series. In contrast, Wavelet Transform (WT) method is widely used to investigate the self-similar processes, as the self-similarity properties exist within the subbands. Therefore, a combination of these two approaches, DFA and WPT, is promising for rigorous investigation of such a system. In this paper a new methodology, so-called wavelet DFA, is introduced and interpreted to evaluate this idea. This approach, further than identifying self-similarity properties, enable us to detect and capture the chaos-periodic transitions, band merging, and internal crisis in systems that become chaotic through period-doubling phenomena. Changes of wavelet DFA exponent have been compared with that of Lyapunov and DFA through Logistic, Sine, Gaussian, Cubic, and Quartic Maps. Furthermore, the potential capabilities of this new exponent have been presented. © 2016 World Scientific Publishing Company.
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