Nonlinear Dynamics, Chaos, and Instability Control in Chemical Reactions

Dynamic systems play a crucial role in numerous fields such as biology, electricity, economics, mechanics, and chemical reactions. This chapter explores nonlinear theory within dynamic systems, focusing on the Brusselator, an autocatalytic and oscillating chemical reaction. The goal is to design a robust controller to manage the chaotic behavior of the Brusselator. Discrete-time sliding mode variable structure control is employed, applied to a linearized a chemical system, and includes a control signal that influences the dynamics. This strategy drives the system state to a sliding surface, maintaining stability despite uncertainties. Results compare open-loop and controlled scenarios, illustrating state variable evolutions, control signals, sliding surfaces, and trajectories. The equilibrium point shows convergence only under the designed control. This study provides a robust solution for the Brusselator’s chaotic behavior, demonstrating the effectiveness of control in maintaining stability and performance. Additionally, we emphasize the potential of this approach to be applied to other problems in the field of chemical systems and autocatalytic reactions.