Nonlinear dynamics and intelligent control of a novel 4D chaotic monetary model with expectation index using SRBF neural networks for sustainable economic stability

Muhamad Deni Johansyah; Bob Foster; Yulian Zifar Ayustira; Rameshbabu Ramar; Seyed Mohammad Hamidzadeh; Aceng Sambas; Muhamad Deni Johansyah; Bob Foster; Yulian Zifar Ayustira; Rameshbabu Ramar; Seyed Mohammad Hamidzadeh; Aceng Sambas

doi:10.3934/math.2026367

AIMS Mathematics

2026, Volume 11, Issue 4: 8903-8925. doi: 10.3934/math.2026367

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Nonlinear dynamics and intelligent control of a novel 4D chaotic monetary model with expectation index using SRBF neural networks for sustainable economic stability

1.
Department of Mathematics, Universitas Padjadjaran, Jatinangor Sumedang 45363, Indonesia
2.
Faculty of Business and Economics, Universitas Informatika dan Bisnis Indonesia, Bandung 40285, Indonesia
3.
Manager of Macroprudential Policy Department, Bank Indonesia, Jakarta 10350, Indonesia
4.
Department of Electronics and Communication Engineering, V. S. B. Engineering College, Karur, Tamilnadu 639111, India
5.
Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran
6.
Artificial Intelligence Research Centre for Islam Sustainability (AIRIS), Universiti Sultan Zainal Abidin, Gongbadak, Terengganu 21300, Malaysia
7.
Department of Mathematical Sciences, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu 602105, India
8.
Department of Mechanical Engineering, Universitas Muhamadiyah Tasikmalaya, Tamansari Gobras, 46196, Tasikmalaya, Indonesia

Received: 01 February 2026 Revised: 11 March 2026 Accepted: 17 March 2026 Published: 01 April 2026
MSC : 37D45, 37M10, 68T07, 91B62, 93C10

In this paper, we proposed and analyzed a novel chaotic monetary model by extending Lazureanu's three-dimensional economic system through the introduction of a fourth state variable, the Expectation Index (E_i), which captures psychological and behavioral dynamics in financial decision-making. The modified system exhibits rich dynamical features such as chaos, multistability, coexisting attractors, and complex bifurcation behavior. Key parameters influencing chaotic regimes were investigated through bifurcation diagrams and Lyapunov exponent spectra. Furthermore, the model's behavior was controlled using amplitude scaling and DC offset boosting techniques without altering its chaotic structure. To suppress chaos and achieve stabilization, a Supervised Radial Basis Function Neural Network (SRBFNN) controller was designed. The SRBFNN was trained using system error signals, achieving extremely low mean squared error (MSE) values: 1.14543×10⁻²¹, 1.7698×10⁻²¹, 2.38218×10⁻¹⁹, and 6.16987×10⁻²⁰ across the four networks. Simulation results demonstrated that the SRBFNN effectively eliminates chaotic behavior and drives the system toward desired equilibrium states with high accuracy and stability.
- chaotic monetary model,
- expectation index,
- SRBFNN,
- nonlinear control,
- economic sustainability
Citation: Muhamad Deni Johansyah, Bob Foster, Yulian Zifar Ayustira, Rameshbabu Ramar, Seyed Mohammad Hamidzadeh, Aceng Sambas. Nonlinear dynamics and intelligent control of a novel 4D chaotic monetary model with expectation index using SRBF neural networks for sustainable economic stability[J]. AIMS Mathematics, 2026, 11(4): 8903-8925. doi: 10.3934/math.2026367

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Abstract

In this paper, we proposed and analyzed a novel chaotic monetary model by extending Lazureanu's three-dimensional economic system through the introduction of a fourth state variable, the Expectation Index (E_i), which captures psychological and behavioral dynamics in financial decision-making. The modified system exhibits rich dynamical features such as chaos, multistability, coexisting attractors, and complex bifurcation behavior. Key parameters influencing chaotic regimes were investigated through bifurcation diagrams and Lyapunov exponent spectra. Furthermore, the model's behavior was controlled using amplitude scaling and DC offset boosting techniques without altering its chaotic structure. To suppress chaos and achieve stabilization, a Supervised Radial Basis Function Neural Network (SRBFNN) controller was designed. The SRBFNN was trained using system error signals, achieving extremely low mean squared error (MSE) values: 1.14543×10⁻²¹, 1.7698×10⁻²¹, 2.38218×10⁻¹⁹, and 6.16987×10⁻²⁰ across the four networks. Simulation results demonstrated that the SRBFNN effectively eliminates chaotic behavior and drives the system toward desired equilibrium states with high accuracy and stability.

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