A Chaotic Butterfly Attractor Model for Economic Stability Assessment in Financial Systems
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...
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2025-05-01
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| author | Muhamad Deni Johansyah Sundarapandian Vaidyanathan Khaled Benkouider Aceng Sambas Chittineni Aruna Sarath Kumar Annavarapu Endang Rusyaman Alit Kartiwa |
| author_facet | Muhamad Deni Johansyah Sundarapandian Vaidyanathan Khaled Benkouider Aceng Sambas Chittineni Aruna Sarath Kumar Annavarapu Endang Rusyaman Alit Kartiwa |
| author_sort | Muhamad Deni Johansyah |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mn>1</mn></msub><mo>=</mo><mn>3.5547</mn><mo>,</mo></mrow></semantics></math></inline-formula> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mn>2</mn></msub><mo>=</mo><mn>0</mn><mo>,</mo></mrow></semantics></math></inline-formula> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mn>3</mn></msub><mo>=</mo><mo>−</mo><mn>22.5642</mn></mrow></semantics></math></inline-formula>, indicating a positive Maximal Lyapunov Exponent (MLE) that confirms chaos. The Kaplan–Yorke Dimension (KYD) is determined as D<sub>k</sub> = 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. |
| format | Article |
| id | doaj-art-357eb3067f3c4081aebd3a1cef36af49 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
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| spelling | doaj-art-357eb3067f3c4081aebd3a1cef36af492025-08-20T03:14:36ZengMDPI AGMathematics2227-73902025-05-011310163310.3390/math13101633A Chaotic Butterfly Attractor Model for Economic Stability Assessment in Financial SystemsMuhamad Deni Johansyah0Sundarapandian Vaidyanathan1Khaled Benkouider2Aceng Sambas3Chittineni Aruna4Sarath Kumar Annavarapu5Endang Rusyaman6Alit Kartiwa7Department of Mathematics, Universitas Padjadjaran, Jatinangor, Sumedang 45363, IndonesiaCentre for Control Systems, Vel Tech University, Avadi Chennai 600062, Tamil Nadu, IndiaDepartment of Electronics, Faculty of Technology, Badji-Mokhtar University, B.P. 12, Sidi Ammar, Annaba 23000, AlgeriaFaculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Besut Campus, Besut 22200, MalaysiaDepartment of Computer Science and Engineering, KKR & KSR Institute of Technology and Sciences, Guntur 522017, Andhra Pradesh, IndiaDepartment of Electronics and Communication Engineering, KKR & KSR Institute of Technology and Sciences, Vinjanampadu, Vatticherukuru Mandal, Guntur 522017, Andhra Pradesh, IndiaDepartment of Mathematics, Universitas Padjadjaran, Jatinangor, Sumedang 45363, IndonesiaDepartment of Mathematics, Universitas Padjadjaran, Jatinangor, Sumedang 45363, IndonesiaThis 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mn>1</mn></msub><mo>=</mo><mn>3.5547</mn><mo>,</mo></mrow></semantics></math></inline-formula> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mn>2</mn></msub><mo>=</mo><mn>0</mn><mo>,</mo></mrow></semantics></math></inline-formula> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mn>3</mn></msub><mo>=</mo><mo>−</mo><mn>22.5642</mn></mrow></semantics></math></inline-formula>, indicating a positive Maximal Lyapunov Exponent (MLE) that confirms chaos. The Kaplan–Yorke Dimension (KYD) is determined as D<sub>k</sub> = 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.https://www.mdpi.com/2227-7390/13/10/1633financial risk systemchaotic butterfly attractoreconomic stabilitymultistability |
| spellingShingle | Muhamad Deni Johansyah Sundarapandian Vaidyanathan Khaled Benkouider Aceng Sambas Chittineni Aruna Sarath Kumar Annavarapu Endang Rusyaman Alit Kartiwa A Chaotic Butterfly Attractor Model for Economic Stability Assessment in Financial Systems Mathematics financial risk system chaotic butterfly attractor economic stability multistability |
| title | A Chaotic Butterfly Attractor Model for Economic Stability Assessment in Financial Systems |
| title_full | A Chaotic Butterfly Attractor Model for Economic Stability Assessment in Financial Systems |
| title_fullStr | A Chaotic Butterfly Attractor Model for Economic Stability Assessment in Financial Systems |
| title_full_unstemmed | A Chaotic Butterfly Attractor Model for Economic Stability Assessment in Financial Systems |
| title_short | A Chaotic Butterfly Attractor Model for Economic Stability Assessment in Financial Systems |
| title_sort | chaotic butterfly attractor model for economic stability assessment in financial systems |
| topic | financial risk system chaotic butterfly attractor economic stability multistability |
| url | https://www.mdpi.com/2227-7390/13/10/1633 |
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