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

IF 2.1 4区化学 Q4 CHEMISTRY, PHYSICAL

Reaction Kinetics, Mechanisms and Catalysis Pub Date : 2026-06-03 DOI:10.1007/s11144-026-03160-7

Kumera Takele Yadeta, Mitiku Daba Firdi, Tamirat Temesgen Dufera

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引用次数: 0

Abstract

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 \(L_1\) 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.

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三维分数阶brusselator系统的稳定性分析和分数阶hopf分岔

本研究利用卡普托分数阶导数考察了三维分数阶Brusselator系统的动力学，该系统考虑了经典模型中缺失的记忆和遗传效应。导出平衡点并线性化，利用matgnon准则分析了局部稳定性，突出了分数阶对稳定区域的影响。利用分数阶Hopf分岔理论研究了振动的出现，并建立了分岔的条件。在适当的条件下，利用基于lyapunov的方法验证了系统的全局渐近稳定性。基于\(L_1\)近似方法的数值模拟验证了理论结果，并说明了从稳定平衡到振荡行为的转变。总体而言，结果表明分数阶建模提供了更好的稳定性和更丰富的动力学，使其成为分析非线性化学反应系统的有效框架。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Reaction Kinetics, Mechanisms and Catalysis CHEMISTRY, PHYSICAL-

CiteScore

3.30

自引率

5.60%

发文量

201

审稿时长

2.8 months

期刊介绍： Reaction Kinetics, Mechanisms and Catalysis is a medium for original contributions in the following fields: -kinetics of homogeneous reactions in gas, liquid and solid phase; -Homogeneous catalysis; -Heterogeneous catalysis; -Adsorption in heterogeneous catalysis; -Transport processes related to reaction kinetics and catalysis; -Preparation and study of catalysts; -Reactors and apparatus. Reaction Kinetics, Mechanisms and Catalysis was formerly published under the title Reaction Kinetics and Catalysis Letters.