Exploring Chaos and Stability in a 3-D Finance Model with Absolute Function Nonlinearity

Muhamad Deni Johansyah (muhamad.deni@unpad.ac.id), Sundarapandian Vaidyanathan, Khaled Benkouider, Aceng Sambas, Kandimalla Mallikarjuna Rao and Katuru Anjaneyulu
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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: Laboratory of Automatic and Signals of Annaba (LASA), Badji Mokhtar-Annaba University, P.O. Box 12, Annaba 23000, Algeria
Aceng Sambas: Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Besut Campus, Besut 22200, Malaysia
Kandimalla Mallikarjuna Rao: Department of Electronics and Communication Engineering, KKR & KSR Institute of Technology and Sciences, Guntur 522017, Andhra Pradesh, India
Katuru Anjaneyulu: Department of Electronics and Communication Engineering, KITS Akshar Institute of Technology, Yanamadala, Guntur 522019, Andhra Pradesh, India

Mathematics, 2025, vol. 13, issue 5, 1-16

Abstract: This paper introduces a novel chaotic finance system derived by incorporating a modeling uncertainty with an absolute function nonlinearity into existing financial systems. The new system, based on the works of Gao and Ma, and Vaidyanathan et al., demonstrates enhanced chaotic behavior with a maximal Lyapunov exponent (MLE) of 0.1355 and a fractal Lyapunov dimension of 2.3197. These values surpass those of the Gao-Ma system (MLE = 0.0904, Lyapunov dimension = 2.2296) and the Vaidyanathan system (MLE = 0.1266, Lyapunov dimension = 2.2997), signifying greater complexity and unpredictability. Through parameter analysis, the system transitions between periodic and chaotic regimes, as confirmed by bifurcation diagrams and Lyapunov exponent spectra. Furthermore, multistability is demonstrated with coexisting chaotic attractors for p = 0.442 and periodic attractors for p = 0.48. The effects of offset boosting control are explored, with attractor positions adjustable by varying a control parameter k , enabling transitions between bipolar and unipolar chaotic signals. These findings underline the system’s potential for advanced applications in secure communications and engineering, providing a deeper understanding of chaotic finance models.

Keywords: chaos; chaotic attractors; multistability; offset boosting (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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