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<p>Financial systems often exhibit complex, nonlinear behavior influenced by multiple interrelated economic factors. In this paper, a four-dimensional financial model is developed, incorporating the money supply as a new factor alongside interest rate, investment demand, and the price index. The model is initially formulated in integer order and later extended to fractional order to capture the memory effects characteristic of real-world financial processes. A comprehensive dynamic analysis is performed to investigate equilibrium points, stability conditions, and the impact of varying monetary injection efficiency. The effect of fractional order variation on system dynamics is also examined to understand its role in stability and complexity. To address instability, a feedback control strategy is proposed within the fractional framework to regulate the system’s behavior. Numerical simulations are used to validate the theoretical approach and demonstrate the potential utility of the control mechanism in maintaining financial system stability.</p>

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A study on a chaotic financial system with fractional-order dynamics and control

  • 期刊论文

  • 发表日期：

    2026年7月21日

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  • Lovely Borah,
  • Kaushik Dehingia,
  • Mohammed Almakki,
  • Hemanta Kumar Sarmah,
  • Kamyar Hosseini

摘要

Financial systems often exhibit complex, nonlinear behavior influenced by multiple interrelated economic factors. In this paper, a four-dimensional financial model is developed, incorporating the money supply as a new factor alongside interest rate, investment demand, and the price index. The model is initially formulated in integer order and later extended to fractional order to capture the memory effects characteristic of real-world financial processes. A comprehensive dynamic analysis is performed to investigate equilibrium points, stability conditions, and the impact of varying monetary injection efficiency. The effect of fractional order variation on system dynamics is also examined to understand its role in stability and complexity. To address instability, a feedback control strategy is proposed within the fractional framework to regulate the system’s behavior. Numerical simulations are used to validate the theoretical approach and demonstrate the potential utility of the control mechanism in maintaining financial system stability.