Turing Pattern Dynamics of the Oregonator Model Based on PD Control Strategy

Currently, there have been numerous remarkable achievements in the spatiotemporal dynamics research of chemical reaction-diffusion models. However, the existing literature on the control of spatiotemporal dynamics in these models is quite limited. Therefore, we propose a proportional-derivative (PD) control strategy for effective control of the spatiotemporal dynamics of the Oregonator chemical reaction-diffusion models under the influence of cross-diffusion. This control strategy aims to both suppress Turing instability in the system and induce changes in the pattern structures of the system. In this study, we utilize linear stability analysis to derive conditions for the occurrence of luring instability in the model. Through numerical simulations, we validate the significant impact of the PD controller on the spatiotemporal dynamics of the model.