Dynamics and Stabilization of Chaotic Monetary System Using Radial Basis Function Neural Network Control
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 beh...
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| Format: | Article |
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MDPI AG
2024-12-01
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| Series: | Mathematics |
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| author | Muhamad Deni Johansyah Aceng Sambas Fareh Hannachi Seyed Mohamad Hamidzadeh Volodymyr Rusyn Monika Hidayanti Bob Foster Endang Rusyaman |
| author_facet | Muhamad Deni Johansyah Aceng Sambas Fareh Hannachi Seyed Mohamad Hamidzadeh Volodymyr Rusyn Monika Hidayanti Bob Foster Endang Rusyaman |
| author_sort | Muhamad Deni Johansyah |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5566c5725540423fa065253f8a8871b7 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-5566c5725540423fa065253f8a8871b72025-08-20T02:43:42ZengMDPI AGMathematics2227-73902024-12-011224397710.3390/math12243977Dynamics and Stabilization of Chaotic Monetary System Using Radial Basis Function Neural Network ControlMuhamad Deni Johansyah0Aceng Sambas1Fareh Hannachi2Seyed Mohamad Hamidzadeh3Volodymyr Rusyn4Monika Hidayanti5Bob Foster6Endang Rusyaman7Department of Mathematics, Universitas Padjadjaran, Jatinangor, Sumedang 45363, IndonesiaFaculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Campus Besut, Terengganu 22200, MalaysiaDepartment of Managment Sciences, Echahid Cheikh Larbi Tebessi University, Tebessa 12002, AlgeriaDepartment of Electrical Engineering, Khorasan Institute of Higher Education, Mashhad 91898, IranDepartment of Radio Engineering and Information Security, Yuriy Fedkovych Chernivtsi National University, 58012 Chernivtsi, UkraineDepartment of Mathematics, Universitas Padjadjaran, Jatinangor, Sumedang 45363, IndonesiaFaculty of Business and Economics, Universitas Informatika dan Bisnis Indonesia, Kiaracondong, Bandung 40285, IndonesiaDepartment of Mathematics, Universitas Padjadjaran, Jatinangor, Sumedang 45363, IndonesiaIn 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.https://www.mdpi.com/2227-7390/12/24/3977chaosmonetary systemmultistabilityradial basis function neural network |
| spellingShingle | Muhamad Deni Johansyah Aceng Sambas Fareh Hannachi Seyed Mohamad Hamidzadeh Volodymyr Rusyn Monika Hidayanti Bob Foster Endang Rusyaman Dynamics and Stabilization of Chaotic Monetary System Using Radial Basis Function Neural Network Control Mathematics chaos monetary system multistability radial basis function neural network |
| title | Dynamics and Stabilization of Chaotic Monetary System Using Radial Basis Function Neural Network Control |
| title_full | Dynamics and Stabilization of Chaotic Monetary System Using Radial Basis Function Neural Network Control |
| title_fullStr | Dynamics and Stabilization of Chaotic Monetary System Using Radial Basis Function Neural Network Control |
| title_full_unstemmed | Dynamics and Stabilization of Chaotic Monetary System Using Radial Basis Function Neural Network Control |
| title_short | Dynamics and Stabilization of Chaotic Monetary System Using Radial Basis Function Neural Network Control |
| title_sort | dynamics and stabilization of chaotic monetary system using radial basis function neural network control |
| topic | chaos monetary system multistability radial basis function neural network |
| url | https://www.mdpi.com/2227-7390/12/24/3977 |
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