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Facilitating Joint Chaos and Fractal Analysis of Biosignals through Nonlinear Adaptive Filtering

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  • Jianbo Gao
  • Jing Hu
  • Wen-wen Tung

Abstract

Background: Chaos and random fractal theories are among the most important for fully characterizing nonlinear dynamics of complicated multiscale biosignals. Chaos analysis requires that signals be relatively noise-free and stationary, while fractal analysis demands signals to be non-rhythmic and scale-free. Methodology/Principal Findings: To facilitate joint chaos and fractal analysis of biosignals, we present an adaptive algorithm, which: (1) can readily remove nonstationarities from the signal, (2) can more effectively reduce noise in the signals than linear filters, wavelet denoising, and chaos-based noise reduction techniques; (3) can readily decompose a multiscale biosignal into a series of intrinsically bandlimited functions; and (4) offers a new formulation of fractal and multifractal analysis that is better than existing methods when a biosignal contains a strong oscillatory component. Conclusions: The presented approach is a valuable, versatile tool for the analysis of various types of biological signals. Its effectiveness is demonstrated by offering new important insights into brainwave dynamics and the very high accuracy in automatically detecting epileptic seizures from EEG signals.

Suggested Citation

  • Jianbo Gao & Jing Hu & Wen-wen Tung, 2011. "Facilitating Joint Chaos and Fractal Analysis of Biosignals through Nonlinear Adaptive Filtering," PLOS ONE, Public Library of Science, vol. 6(9), pages 1-8, September.
    • Handle: RePEc:plo:pone00:0024331
    DOI: 10.1371/journal.pone.0024331
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    1. Gao, Jianbo & Fang, Peng & Liu, Feiyan, 2017. "Empirical scaling law connecting persistence and severity of global terrorism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 74-86.
    2. Neelakshi, J. & Rosa, Reinaldo R. & Savio, Siomel & Stephany, Stephan & de Meneses, Francisco C. & Kherani, Esfhan Alam & Muralikrishna, P., 2022. "Multifractal characteristics of the low latitude equatorial ionospheric E–F valley region irregularities," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Wang, Fang & Han, Guosheng, 2023. "Coupling correlation adaptive detrended analysis for multiple nonstationary series," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    4. Marietta Kirchner & Patric Schubert & Magnus Liebherr & Christian T Haas, 2014. "Detrended Fluctuation Analysis and Adaptive Fractal Analysis of Stride Time Data in Parkinson's Disease: Stitching Together Short Gait Trials," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-6, January.
    5. Wu Zhu & Jian-an Fang & Yang Tang & Wenbing Zhang & Wei Du, 2012. "Digital IIR Filters Design Using Differential Evolution Algorithm with a Controllable Probabilistic Population Size," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    6. Anca Tănasie & Raluca Drăcea & Georgiana Raluca Lădaru, 2017. "A Chaos Theory Perspective on International Migration," Sustainability, MDPI, vol. 9(12), pages 1-10, December.
    7. Mihailović, Dragutin T. & Nikolić-Đorić, Emilija & Arsenić, Ilija & Malinović-Milićević, Slavica & Singh, Vijay P. & Stošić, Tatijana & Stošić, Borko, 2019. "Analysis of daily streamflow complexity by Kolmogorov measures and Lyapunov exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 290-303.
    8. He, Hong-di & Wang, Jun-li & Wei, Hai-rui & Ye, Cheng & Ding, Yi, 2016. "Fractal behavior of traffic volume on urban expressway through adaptive fractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 518-525.
    9. Fanglei Wang & Jianbo Gao & Yuting Liu, 2024. "Spatiotemporal evolution of Nigeria’s armed conflicts and terrorism and the associated shift in social perceptions," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-13, December.

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