Finite-time control of the discrete Sel’kov–Schnakenberg model: Synchronization and simulations

This study investigates the finite-time synchronization (FT-sync) of the Selkov–Schnakenberg reaction–diffusion system, utilizing Lyapunov functions and discrete finite-difference methods. Theoretical conditions are derived to achieve synchronization within a finite duration, a concept referred to as (FT-sync), which ensures rapid alignment of system states as opposed to classical asymptotic synchronization. The analysis is supported by numerical simulations that demonstrate the effectiveness of the proposed control strategies in enforcing synchronization under variable initial conditions and system configurations. In addition, the study investigates the impact of system parameters on spatiotemporal dynamics and synchronization patterns. These results hold significant value for practical applications requiring synchronization, such as in chemical reactors and biological systems, while also enriching the theoretical understanding of finite-time dynamics in reaction–diffusion systems.