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<p>The study of bifurcation and chaos in fractional-order dynamical systems finds innovative applications in science and engineering, particularly in chaos-based cryptography for enhanced security. This paper investigates the fractional proto Bhalekar–Gejji (BG) system, a three-dimensional, non-linear dynamical system for chaotic motion. We perform stability analysis, plot bifurcation diagrams and explore chaotic regions. We observe that in fractional proto-BG system an equilibrium point undergoes a subcritical Hopf bifurcation leading to chaos. Further we determine Hopf critical values, plot corresponding curves, and compute Lyapunov coefficients. It is observed that chaos diminishes as the fractional order decreases, with a threshold value of 0.977 for the order of the derivative, below which chaos ceases to exist.</p>

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Analysis of the fractional proto Bhalekar–Gejji system

  • 期刊论文

  • 发表日期：

    2025年7月14日

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  • Rajashree S. Jadhav,
  • Amey S. Deshpande,
  • Varsha Daftardar-Gejji

摘要

The study of bifurcation and chaos in fractional-order dynamical systems finds innovative applications in science and engineering, particularly in chaos-based cryptography for enhanced security. This paper investigates the fractional proto Bhalekar–Gejji (BG) system, a three-dimensional, non-linear dynamical system for chaotic motion. We perform stability analysis, plot bifurcation diagrams and explore chaotic regions. We observe that in fractional proto-BG system an equilibrium point undergoes a subcritical Hopf bifurcation leading to chaos. Further we determine Hopf critical values, plot corresponding curves, and compute Lyapunov coefficients. It is observed that chaos diminishes as the fractional order decreases, with a threshold value of 0.977 for the order of the derivative, below which chaos ceases to exist.