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

Muhamad Deni Johansyah (), Aceng Sambas, Fareh Hannachi, Seyed Mohamad Hamidzadeh, Volodymyr Rusyn, Monika Hidayanti, Bob Foster and Endang Rusyaman
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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
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

Mathematics, 2024, vol. 12, issue 24, 1-20

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.

Keywords: chaos; monetary system; multistability; radial basis function neural network (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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