article · Partial Differential Equations in Applied Mathematics
A new hyperchaotic financial model incorporating profit margin has been formulated to examine complex dynamics in economic systems. Using the Adomian Decomposition Method, the Caputo fractional-order system was solved, establishing formal mathematical criteria for the existence and uniqueness of its exact solutions. Computational tools, including Lyapunov exponents, bifurcation diagrams, complexity analysis, and the 0-1 test, were applied to assess the system behaviour. These evaluations confirmed the presence of periodic, chaotic, and hyperchaotic states within the model. To manage these irregular fluctuations, a control strategy was formulated using linear feedback control combined with the Laplace transform. Numerical simulations verified the analytical findings, demonstrating close alignment between theoretical predictions and simulated behaviours, which confirms the mathematical viability of the control technique for stabilising such complex financial formulations.
Financial systems often display highly volatile and unpredictable behaviours that resist standard economic models. Demonstrating how hyperchaotic dynamics emerge in models with profit margins, and proving that these fluctuations can be mathematically controlled using linear feedback mechanisms, helps researchers and quantitative analysts better understand, model, and potentially stabilise extreme instabilities in complex financial frameworks.
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This research study proposes a novel hyperchaotic finance system with profit margin and then utilizes the Adomian Decomposition Method (ADM) to tackle the solution of the associated Caputo-derivative based fractional-order hyperchaotic finance system with profit margin. Numerical simulations and analyses, such as the evaluation of Lyapunov exponents (LE), the creation of bifurcation diagrams (BD), the complexity analysis (CA), and the 0-1 test, are used to get a full picture of the system. The results of our study demonstrate the occurrence of periodic, chaotic, and hyperchaotic dynamics in the system. Furthermore, the overall criteria for the existence and the uniqueness of the exact solutions for Caputo fractional-order models are presented. In addition, we present a control methodology for the fractional-order hyperchaotic financial system utilizing the Laplace transform and linear feedback control. Significantly, our research showcases a noteworthy correlation between the analytical results and numerical simulations, emphasizing the soundness and effectiveness of our methodology.
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DOI: 10.1016/j.padiff.2023.100612
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