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<p>This study investigates the dynamical behavior and control strategies of a modified Brusselator model in the context of sustained chemical reactions. A new dimensionless model incorporating dynamic inflow of reactant species is developed to better capture real world chemical environments. The system of nonlinear differential equations under consideration introduces a coupling with an additional variable <i>z</i>, representing an intermediate species or external influence, thereby extending the classical Brusselator model. We analyze the equilibrium points and explore the local and global bifurcation phenomena that emerge due to variations in key parameters <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> and <i>m</i> with bifurcation behavior which shifts for different values of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>. Furthermore, we develop and implement an adaptive control mechanism to regulate the system dynamics, ensuring desired behavior even in the presence of nonlinear instabilities. Numerical simulations, using MATLAB’s ode45 solver, demonstrate how varying parameters influence the system’s behavior and validate the effectiveness of the proposed adaptive controller. The results provide insights into managing complex chemical reactions through robust control methods, as the tracking error converges to zero and parameter estimation stabilizes over time.</p>

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Analyzing bifurcation and adaptive control mechanisms of the Brusselator system in a maintained chemical reaction

  • 期刊论文

  • 发表日期：

    2025年9月22日

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

摘要

This study investigates the dynamical behavior and control strategies of a modified Brusselator model in the context of sustained chemical reactions. A new dimensionless model incorporating dynamic inflow of reactant species is developed to better capture real world chemical environments. The system of nonlinear differential equations under consideration introduces a coupling with an additional variable z, representing an intermediate species or external influence, thereby extending the classical Brusselator model. We analyze the equilibrium points and explore the local and global bifurcation phenomena that emerge due to variations in key parameters \(\alpha\) α and m with bifurcation behavior which shifts for different values of \(\alpha\) α . Furthermore, we develop and implement an adaptive control mechanism to regulate the system dynamics, ensuring desired behavior even in the presence of nonlinear instabilities. Numerical simulations, using MATLAB’s ode45 solver, demonstrate how varying parameters influence the system’s behavior and validate the effectiveness of the proposed adaptive controller. The results provide insights into managing complex chemical reactions through robust control methods, as the tracking error converges to zero and parameter estimation stabilizes over time.