A Chaotic Butterfly Attractor Model for Economic Stability Assessment in Financial Systems

Muhamad Deni Johansyah (), Sundarapandian Vaidyanathan, Khaled Benkouider, Aceng Sambas, Chittineni Aruna, Sarath Kumar Annavarapu, Endang Rusyaman and Alit Kartiwa
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Muhamad Deni Johansyah: Department of Mathematics, Universitas Padjadjaran, Jatinangor, Sumedang 45363, Indonesia
Sundarapandian Vaidyanathan: Centre for Control Systems, Vel Tech University, Avadi Chennai 600062, Tamil Nadu, India
Khaled Benkouider: Department of Electronics, Faculty of Technology, Badji-Mokhtar University, B.P. 12, Sidi Ammar, Annaba 23000, Algeria
Aceng Sambas: Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Besut Campus, Besut 22200, Malaysia
Chittineni Aruna: Department of Computer Science and Engineering, KKR & KSR Institute of Technology and Sciences, Guntur 522017, Andhra Pradesh, India
Sarath Kumar Annavarapu: Department of Electronics and Communication Engineering, KKR & KSR Institute of Technology and Sciences, Vinjanampadu, Vatticherukuru Mandal, Guntur 522017, Andhra Pradesh, India
Endang Rusyaman: Department of Mathematics, Universitas Padjadjaran, Jatinangor, Sumedang 45363, Indonesia
Alit Kartiwa: Department of Mathematics, Universitas Padjadjaran, Jatinangor, Sumedang 45363, Indonesia

Mathematics, 2025, vol. 13, issue 10, 1-14

Abstract: This paper introduces a novel three-dimensional financial risk system that exhibits complex dynamical behaviors, including chaos, multistability, and a butterfly attractor. The proposed system is an extension of the Zhang financial risk model (ZFRM), with modifications that enhance its applicability to real-world economic stability assessments. Through numerical simulations, we confirm the system’s chaotic nature using Lyapunov exponents (LE), with values calculated as L 1 = 3.5547 , L 2 = 0 , L 3 = − 22.5642 , indicating a positive Maximal Lyapunov Exponent (MLE) that confirms chaos. The Kaplan–Yorke Dimension (KYD) is determined as D k = 2.1575, reflecting the system’s fractal characteristics. Bifurcation analysis (BA) reveals parameter ranges where transitions between periodic, chaotic, and multistable states occur. Additionally, the system demonstrates coexisting attractors, where different initial conditions lead to distinct long-term behaviors, emphasizing its sensitivity to market fluctuations. Offset Boosting Control (OBC) is implemented to manipulate the chaotic attractor, shifting its amplitude without altering the underlying system dynamics. These findings provide deeper insights into financial risk modeling and economic stability, with potential applications in financial forecasting, risk assessment, and secure economic data transmission.

Keywords: financial risk system; chaotic butterfly attractor; economic stability; multistability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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