Synchronization in Finite Time of Discrete Reaction-Diffusion Models

Abstract

This study investigates finite-time synchronization in discrete reaction-diffusion systems focusing on an epidemic reaction-diffusion model. Employing Lyapunov-based methods and tailored control strategies, we derive theoretical conditions to ensure finite-time synchronization between master and slave systems. Explicit bounds on settling time are established, addressing challenges posed by system nonlinearities, spatial dynamics, and parameter variations. Numerical simulations validate the theoretical findings, confirming rapid convergence and synchronization within the predicted time frame. The results highlight the robustness of the proposed approach against discretization errors and parameter uncertainties, making it applicable to various biological, chemical, and physical systems. Future extensions may include fractional-order dynamics, complex network topologies, and adaptive control strategies.