Analysis of Stability and Adaptive Control of Brusselator System in Maintained Chemical Reaction

This paper investigates the stability and adaptive control of a three-dimensional maintained Brusselator system modeling autocatalytic chemical reactions with continuous inflow. Unlike the classical Brusselator, where reactant concentrations are assumed constant, the proposed model explicitly incorporates a sustained inflow of Component B, leading to richer and potentially unstable nonlinear dynamics. Equilibrium and eigenvalue analyses reveal that specific inflow rates induce oscillatory and unstable behavior. To overcome this limitation, a nonlinear Lyapunov-based adaptive control strategy is developed directly from the full nonlinear dynamics, without linearization or exact knowledge of system parameters. The proposed controller guarantees global exponential convergence of all state variables to desired steady states under parametric uncertainty. Numerical simulations confirm robust stabilization and fast convergence, demonstrating the effectiveness of the proposed approach for maintained chemical reaction systems.