Synchronization of Reaction-Diffusion Systems With Time Delay Via The Lyapunov-Razumikhin Method

In this paper, a boundary control method for synchronizing a drive reaction-diffusion system and a response reaction-diffusion system is proposed. For the reaction-diffusion systems with time delay, we apply the backstepping method to design a boundary control law and prove the uniform asymptotic stability of the error system between the drive and response systems by using the Lyapunov-Razumikhin method. Finally, the feasibility is verified through numerical simulations.