Optimization of Spatiotemporal Dynamics in the Gierer-Meinhardt Model using a PD Control Strategy

While the spatiotemporal dynamics of reaction-diffusion systems have been extensively studied, the control of spatiotemporal evolution dynamics in reaction-diffusion systems remains an unresolved issue. The Gierer-Meinhardt reaction-diffusion system is a typical mathematical model to describe chemical and biological phenomena. By controlling the Turing patterns within the system, it is possible to make relatively accurate predictions and regulate the development trends of the reactants. However, there has been relatively limited research on the control of Turing patterns in Gierer-Meinhardt systems. In this paper, we propose a proportional differential control strategy for the Gierer-Meinhardt system with diffusion terms, aiming to regulate the spatiotemporal dynamics of the model through the controller.