Spatiotemporal dynamics optimization of a Gierer-Meinhardt system based on PD control strategy

The dynamic control of ordinary differential systems has yielded fruitful results, but the spatiotemporal control of partial differential systems is still a problem to be solved. The Gierer-Meinhardt system is a partial differential system that has been extensively studied in reaction-diffusion theory. It can plausibly explain many phenomena in biology and chemistry. In this paper we investigate the effect of PD controller on the dynamics of spatiotemporal evolution of the Gierer-Meinhardt system. The conditions under which Turing instability occurs before and after the Gierer-Meinhardt system is controlled are obtained by linear stability analysis. Numerical simulations show that PD controller promotes the occurrence of Turing instability in the Gierer-Meinhardt system. Furthermore, it can change the spatial structure and speed up the formation of Turing pattrens.