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<p>This study examines the dynamics of a three-dimensional fractional-order Brusselator system using the Caputo fractional derivative, which accounts for memory and hereditary effects absent in classical models. The equilibrium point is derived and linearized, and local stability is analyzed using Matignon’s criterion, highlighting the influence of the fractional order on the stability region. The emergence of oscillations is investigated via fractional-order Hopf bifurcation theory, and conditions for bifurcation are established. A Lyapunov-based approach is used to confirm global asymptotic stability under suitable conditions. Numerical simulations based on the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> approximation method validate the theoretical results and illustrate the transition from stable equilibrium to oscillatory behavior. Overall, the results demonstrate that fractional-order modeling provides improved stability and richer dynamics, making it an effective framework for analyzing nonlinear chemical reaction systems.</p>

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Stability analysis and fractional hopf bifurcation in a three-dimensional fractional-order brusselator system

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Kumera Takele Yadeta,
  • Mitiku Daba Firdi,
  • Tamirat Temesgen Dufera

摘要

This study examines the dynamics of a three-dimensional fractional-order Brusselator system using the Caputo fractional derivative, which accounts for memory and hereditary effects absent in classical models. The equilibrium point is derived and linearized, and local stability is analyzed using Matignon’s criterion, highlighting the influence of the fractional order on the stability region. The emergence of oscillations is investigated via fractional-order Hopf bifurcation theory, and conditions for bifurcation are established. A Lyapunov-based approach is used to confirm global asymptotic stability under suitable conditions. Numerical simulations based on the \(L_1\) L 1 approximation method validate the theoretical results and illustrate the transition from stable equilibrium to oscillatory behavior. Overall, the results demonstrate that fractional-order modeling provides improved stability and richer dynamics, making it an effective framework for analyzing nonlinear chemical reaction systems.