Optimization of Pattern Dynamics of FitzHugh-Nagumo System Based on PD Control Strategy

The FitzHugh-Nagumo system is a chemical and biological reaction diffusion control system. At present, domestic and foreign studies are only limited to the study of the Turing-Hopf bifurcation kinetics and diffusion effects of the FitzHugh-Nagumo system. However, there are fewer reports on the effect of the control strategy on the spatiotemporal patterns. In this paper, the effect of proportional-derivative (PD) control strategy on the spatiotemporal evolution dynamics of the FitzHugh-Nagumo system is investigated. Using the linear stability analysis method, the stability conditions for the system without diffusion and the Turing instability conditions for the diffusion system are established. And using simulation we verify the feasibility of the theoretical analysis. The results show that a change in the proportional coefficient leads to a change in the Turing bifurcation threshold. In addition the PD controller can inhibit and promote the occurrence of Turing instability in the FitzHugh-Nagumo system.