Finite-time synchronization of the discrete reaction-diffusion Fitzhugh-Nagumo model

The objective of this research is to explore finite-time synchronization between two systems characterized by completely unknown parameters. Finite-time synchronization (FTS) has become a focal point of interest in recent years, and this paper focuses specifically on addressing the FTS challenge within the FitzHugh-Nagumo reaction-diffusion model. Initially, we introduce a control technique suitable for a wide range of master-slave configurations. Subsequently, we employ a Lyapunov method to illustrate the finite-time stability of the associated error master-slave systems. Additionally, we establish theoretical findings and demonstrate the practical application of this framework through numerical simulations. Ultimately, these simulations are utilized to validate the finite-time synchronization predictions.