IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v157y2022ics0960077922001187.html
   My bibliography  Save this article

When machine learning meets fractional-order chaotic signals: detecting dynamical variations

Author

Listed:
  • Kavuran, Gürkan

Abstract

The challenge of classifying multivariate time series generated by discrete and continuous dynamical systems according to their chaotic or non-chaotic behavior has been studied extensively in the literature. The examination of noise or the variation of variables that affect a dynamic system's chaoticity will not be beneficial in analyzing structures employing random number generators (RNG) that are already assured to be chaotic. However, detecting the structural changes and their time intervals in deterministic systems with proven chaoticity can contribute to the literature in encryption applications. Machine Learning algorithms provide flexible possibilities to analyze and predict manipulations that may occur in the dynamics of chaotic and complex systems. This study proposes a deep Long-Short-Term-Memory (LSTM) network with a classification process to predict dynamical changes in a fractional-order chaotic (FOC) system. First, the appropriate system parameters are calculated to satisfy the chaotic behavior in the fractional-order Chen system. The predictive-corrective Adams-Bashforth-Moulton algorithm is used to simulate the FOC Chen system in the time domain. The Lyapunov exponents of the system were obtained according to the Wolf method. Next, three different scenarios have been designed to test and demonstrate the effectiveness of the proposed method. Synthetic FOC signals obtained after sub-sampling and statistical feature extraction processes fed the input of the deep bidirectional LSTM (BiLSTM) network to perform the training and testing process. The classification performance for "q" and "c" classes reaches 100% with the proposed model. The overall average testing accuracy, sensitivity, specificity, precision, F1 score and MCC are 98%, 98%, 99.3%, 98.1%, 98%, and 97.3%, respectively. Our results demonstrate the utility of using a deep BiLSTM network for detecting dynamical variations in nonlinear FOC systems.

Suggested Citation

  • Kavuran, Gürkan, 2022. "When machine learning meets fractional-order chaotic signals: detecting dynamical variations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001187
    DOI: 10.1016/j.chaos.2022.111908
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922001187
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.111908?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    2. Ian Stewart, 2000. "The Lorenz attractor exists," Nature, Nature, vol. 406(6799), pages 948-949, August.
    3. Louzzani, Noura & Boukabou, Abdelkrim & Bahi, Halima & Boussayoud, Ali, 2021. "A novel chaos based generating function of the Chebyshev polynomials and its applications in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    5. Asiain, Erick & Garrido, Rubén, 2021. "Anti-Chaos control of a servo system using nonlinear model reference adaptive control," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Lahmiri, Salim & Bekiros, Stelios, 2019. "Cryptocurrency forecasting with deep learning chaotic neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 35-40.
    8. Baris Baykant Alagoz & Gurkan Kavuran & Abdullah Ates & Celaleddin Yeroglu, 2017. "Reference-shaping adaptive control by using gradient descent optimizers," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-20, November.
    9. Xiong, Pei-Ying & Jahanshahi, Hadi & Alcaraz, Raúl & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alsaadi, Fawaz E., 2021. "Spectral Entropy Analysis and Synchronization of a Multi-Stable Fractional-Order Chaotic System using a Novel Neural Network-Based Chattering-Free Sliding Mode Technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ren, Jinfu & Liu, Yang & Liu, Jiming, 2023. "Chaotic behavior learning via information tracking," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Izadbakhsh, Alireza & Nikdel, Nazila, 2021. "Chaos synchronization using differential equations as extended state observer," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    2. Bekiros, Stelios & Yao, Qijia & Mou, Jun & Alkhateeb, Abdulhameed F. & Jahanshahi, Hadi, 2023. "Adaptive fixed-time robust control for function projective synchronization of hyperchaotic economic systems with external perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    3. Ouannas, Adel & Batiha, Iqbal M. & Bekiros, Stelios & Liu, Jinping & Jahanshahi, Hadi & Aly, Ayman A. & Alghtani, Abdulaziz H., 2021. "Synchronization of the glycolysis reaction-diffusion model via linear control law," LSE Research Online Documents on Economics 112776, London School of Economics and Political Science, LSE Library.
    4. Ge, Zheng-Ming & Yi, Chang-Xian, 2007. "Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 42-61.
    5. El-Dessoky Ahmed, M.M. & Altaf Khan, Muhammad, 2020. "Modeling and analysis of the polluted lakes system with various fractional approaches," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    6. Méndez-Gordillo, Alma Rosa & Cadenas, Erasmo, 2021. "Wind speed forecasting by the extraction of the multifractal patterns of time series through the multiplicative cascade technique," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    7. Chowdhury, Reaz & Rahman, M. Arifur & Rahman, M. Sohel & Mahdy, M.R.C., 2020. "An approach to predict and forecast the price of constituents and index of cryptocurrency using machine learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    8. Balcı, Ercan & Öztürk, İlhan & Kartal, Senol, 2019. "Dynamical behaviour of fractional order tumor model with Caputo and conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 43-51.
    9. Atangana, Abdon, 2018. "Blind in a commutative world: Simple illustrations with functions and chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 347-363.
    10. Flori, Andrea, 2019. "News and subjective beliefs: A Bayesian approach to Bitcoin investments," Research in International Business and Finance, Elsevier, vol. 50(C), pages 336-356.
    11. Kate Murray & Andrea Rossi & Diego Carraro & Andrea Visentin, 2023. "On Forecasting Cryptocurrency Prices: A Comparison of Machine Learning, Deep Learning, and Ensembles," Forecasting, MDPI, vol. 5(1), pages 1-14, January.
    12. Yan, Fang & Hou, Xiaorong & Tian, Tingting & Chen, Xiaojie, 2023. "Nonlinear model reference adaptive control approach for governance of the commons in a feedback-evolving game," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    13. Hakan Pabuccu & Adrian Barbu, 2023. "Feature Selection with Annealing for Forecasting Financial Time Series," Papers 2303.02223, arXiv.org, revised Feb 2024.
    14. Momani, Shaher & Odibat, Zaid, 2007. "Numerical comparison of methods for solving linear differential equations of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1248-1255.
    15. Jiale Sheng & Wei Jiang & Denghao Pang & Sen Wang, 2020. "Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel," Mathematics, MDPI, vol. 8(12), pages 1-10, December.
    16. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
    17. Salim Lahmiri, 2020. "A predictive system integrating intrinsic mode functions, artificial neural networks, and genetic algorithms for forecasting S&P500 intra‐day data," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 27(2), pages 55-65, April.
    18. Petráš, Ivo, 2008. "A note on the fractional-order Chua’s system," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 140-147.
    19. Kumar, Sachin & Pandey, Prashant, 2020. "Quasi wavelet numerical approach of non-linear reaction diffusion and integro reaction-diffusion equation with Atangana–Baleanu time fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    20. Ehsan Hoseinzade & Saman Haratizadeh & Arash Khoeini, 2019. "U-CNNpred: A Universal CNN-based Predictor for Stock Markets," Papers 1911.12540, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001187. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.