Empirically developed model of the stirring-controlled Belousov–Zhabotinsky reaction

The Belousov–Zhabotinsky chemical reaction is famous for its oscillatory behavior occurring due to inherent physicochemical processes. Oscillations of the Belousov–Zhabotinsky reaction may be periodic or chaotic, depending on parameters, and these dynamics can be controlled by external impacts such as stirring. The complex behavior, the variability of the oscillatory modes, and controllability make the Belousov–Zhabotinsky reaction an important research subject in many fields of science, including various applications such as chemical computing or smart materials. One of the key limitations for the practical application of this oscillatory reaction is the absence of its exact mathematical model which can reproduce dynamics close to the real chemical process. This work aims to fill this gap by designing a novel model of the Belousov–Zhabotinsky reaction based on experimental data. To solve this task, we designed a complex experimental setup based on a photometric station with controllable stirring mechanisms. We performed two experiments in batch reactors (cuvettes). In the first experiment, we investigated how constant stirring with different rates affects the reaction behavior, and in the second experiment, we periodically stirred the reaction and observed its response. As a result, we found that chemical oscillations in the Belousov–Zhabotinsky reaction are in both cases chaotic, their amplitude depends on stirring more than their period does, and they are highly non-stationary: in the course of the reaction, their sensitivity to stirring decreases, so the oscillations remain controllable only during the first hour. Using a novel two-stage differential equation reconstruction approach, we managed to develop a complex of local dynamical models for the stirring-controlled BZ reaction with good correspondence to the empirical data. The presented models are more consistent with experimentally observed Belousov–Zhabotinsky dynamics than earlier models. The developed model can be used in various applications and extended to a wide class of controlled oscillatory reactions.