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Dynamical Analysis and Adaptive Finite-Time Sliding Mode Control Approach of the Financial Fractional-Order Chaotic System

Author

Listed:
  • Muhamad Deni Johansyah

    (Department of Mathematics, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Aceng Sambas

    (Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya 46196, Indonesia)

  • Saleh Mobayen

    (Department of Electrical Engineering, Faculty of Engineering, University of Zanjan, Zanjan 45371, Iran
    Graduate School of Intelligent Data Science, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 640301, Taiwan)

  • Behrouz Vaseghi

    (Department of Electrical and Computer Engineering, Abhar Branch, Islamic Azad University, Abhar 6134937333, Iran)

  • Saad Fawzi Al-Azzawi

    (Department of Mathematics, University of Mosul, Mosul 00964, Iraq)

  • Sukono

    (Department of Mathematics, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Ibrahim Mohammed Sulaiman

    (School of Quantitative Sciences, Universiti Utara Malaysia, Sintok 06010, Malaysia)

Abstract

In this work, we studied the complex behaviors of the fractional-order financial chaotic system, consisting of a simple, relatively chaotic system with two quadratic nonlinearities (QN) and a sextic nonlinearity (SN). We completed and enriched the results presented in the study of Subartini et al. (2021). As a result of this, our study focused more on the fractional order and adaptive finite-time sliding mode control in the financial risk chaotic system. The dynamical behaviors of the financial chaotic system (FCS) with two QN and an SN were analyzed, and the stability was investigated via the Cardano method. The stability analysis showed that the real part of all the roots was negative, which confirmed the stability of the new system under the typical parameters. By using the MATLAB simulation, these properties were characterized, including the phase portraits, 0-1 test, Poincaré map, bifurcation diagram, and Lyapunov exponent. The analysis showed that the financial risk chaotic system of fractional order was able to exhibit chaotic behavior and periodical behavior. In spite of external perturbations and uncertainty, an adaptive finite-time sliding mode control strategy was devised to guide the states of the financial chaotic system to the origin in a finite amount of time. MATLAB phase plots were employed in this study to illustrate all the main results.

Suggested Citation

  • Muhamad Deni Johansyah & Aceng Sambas & Saleh Mobayen & Behrouz Vaseghi & Saad Fawzi Al-Azzawi & Sukono & Ibrahim Mohammed Sulaiman, 2022. "Dynamical Analysis and Adaptive Finite-Time Sliding Mode Control Approach of the Financial Fractional-Order Chaotic System," Mathematics, MDPI, vol. 11(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:100-:d:1015402
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    References listed on IDEAS

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