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Dynamics and Stabilization of Chaotic Monetary System Using Radial Basis Function Neural Network Control

Author

Listed:
  • Muhamad Deni Johansyah

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

  • Aceng Sambas

    (Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Campus Besut, Terengganu 22200, Malaysia
    Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tamansari Gobras, Tasikmalaya 46196, Indonesia
    Artificial Intelligence for Sutainability and Islamic Research Center (AISIR), Universiti Sultan Zainal Abidin, Gongbadak, Terengganu 21300, Malaysia)

  • Fareh Hannachi

    (Department of Managment Sciences, Echahid Cheikh Larbi Tebessi University, Tebessa 12002, Algeria)

  • Seyed Mohamad Hamidzadeh

    (Department of Electrical Engineering, Khorasan Institute of Higher Education, Mashhad 91898, Iran)

  • Volodymyr Rusyn

    (Department of Radio Engineering and Information Security, Yuriy Fedkovych Chernivtsi National University, 58012 Chernivtsi, Ukraine)

  • Monika Hidayanti

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

  • Bob Foster

    (Faculty of Business and Economics, Universitas Informatika dan Bisnis Indonesia, Kiaracondong, Bandung 40285, Indonesia)

  • Endang Rusyaman

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

Abstract

In this paper, we investigated a three-dimensional chaotic system that models key aspects of a monetary system, including interest rates, investment demand, and price levels. The proposed system is described by a set of autonomous quadratic ordinary differential equations. We analyze the dynamic behavior of this system through equilibrium points and their stability, Lyapunov exponents (LEs), and bifurcation diagrams. The system demonstrates a variety of behaviors, including chaotic, periodic, and equilibrium states depending on parameter values. Additionally, we explore the multistability of the system and present a radial basis function neural network (RBFNN) controller design to stabilize the chaotic behavior. The effectiveness of the controller is validated through numerical simulations, highlighting its potential applications in economic and financial modeling.

Suggested Citation

  • Muhamad Deni Johansyah & Aceng Sambas & Fareh Hannachi & Seyed Mohamad Hamidzadeh & Volodymyr Rusyn & Monika Hidayanti & Bob Foster & Endang Rusyaman, 2024. "Dynamics and Stabilization of Chaotic Monetary System Using Radial Basis Function Neural Network Control," Mathematics, MDPI, vol. 12(24), pages 1-20, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3977-:d:1546491
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    References listed on IDEAS

    as
    1. Paul Yaovi Dousseh & Cyrille Ainamon & Clément Hodévèwan Miwadinou & Adjimon Vincent Monwanou & Jean Bio Chabi Orou, 2021. "Adaptive Control of a New Chaotic Financial System with Integer Order and Fractional Order and Its Identical Adaptive Synchronization," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-15, March.
    2. Li, Qinnan & Li, Ruihong & Huang, Dongmei, 2023. "Dynamic analysis of a new 4D fractional-order financial system and its finite-time fractional integral sliding mode control based on RBF neural network," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    3. Olga Kozlovska & Felix Sadyrbaev & Inna Samuilik, 2023. "A New 3D Chaotic Attractor in Gene Regulatory Network," Mathematics, MDPI, vol. 12(1), pages 1-17, December.
    4. O. Gomes & V. M. Mendes & D. A. Mendes & J. Sousa Ramos, 2007. "Chaotic dynamics in optimal monetary policy," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 195-199, May.
    5. 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.
    6. Zhang, Guoxing & Qian, Pengxiao & Su, Zhaoxian, 2019. "Evolution of fractional-order chaotic economic systems based on non-degenerate equilibrium points," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 219-228.
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