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<p>This paper investigates the hyperchaotic behavior of a newly proposed financial system characterized by cubic nonlinearity and multiple coexisting attractors. The system is modeled using four state variables: interest rate (<i>I</i><sub>r</sub>), investment demand (<i>I</i><sub>d</sub>), price index (<i>P</i><sub>i</sub>), and average profit rate (<i>P</i><sub>m</sub>), governed by nonlinear differential equations. Through Lyapunov exponent analysis, the system is confirmed to exhibit hyperchaos, with computed exponents (LE1, LE2, LE3, LE4) = (0.04, 0.01, 0, -1.166), indicating two positive values and thus high sensitivity to initial conditions. Bifurcation analysis further reveals complex transitions between periodic, chaotic, and hyperchaotic states under varying parameters. To achieve synchronization and control of the hyperchaotic system, a Supervised Radial Basis Function Neural Network (SRBFNN) is implemented. The SRBFNN is trained using classical control methods and successfully stabilizes the system within approximately 5-time units after activation at <i>t</i> = 10. Additionally, the effect of DC offset boosting and amplitude control is analyzed, demonstrating effective regulation of chaotic oscillations. Numerical simulations validate the theoretical findings, highlighting the applicability of SRBFNN-based control in financial modeling and secure data transmission.</p>

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Investigation and SRBFNN-based stabilization of the hyperchaotic behavior in a novel financial system with cubic nonlinearity and multiple coexisting attractors

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Muhamad Deni Johansyah,
  • Aceng Sambas,
  • Rameshbabu Ramar,
  • Seyed Mohamad Hamidzadeh

摘要

This paper investigates the hyperchaotic behavior of a newly proposed financial system characterized by cubic nonlinearity and multiple coexisting attractors. The system is modeled using four state variables: interest rate (Ir), investment demand (Id), price index (Pi), and average profit rate (Pm), governed by nonlinear differential equations. Through Lyapunov exponent analysis, the system is confirmed to exhibit hyperchaos, with computed exponents (LE1, LE2, LE3, LE4) = (0.04, 0.01, 0, -1.166), indicating two positive values and thus high sensitivity to initial conditions. Bifurcation analysis further reveals complex transitions between periodic, chaotic, and hyperchaotic states under varying parameters. To achieve synchronization and control of the hyperchaotic system, a Supervised Radial Basis Function Neural Network (SRBFNN) is implemented. The SRBFNN is trained using classical control methods and successfully stabilizes the system within approximately 5-time units after activation at t = 10. Additionally, the effect of DC offset boosting and amplitude control is analyzed, demonstrating effective regulation of chaotic oscillations. Numerical simulations validate the theoretical findings, highlighting the applicability of SRBFNN-based control in financial modeling and secure data transmission.