<p>Partial differential equations (PDEs) are essential in chemical engineering and other applied sciences for modeling complex systems, such as the glycolysis biochemical pathway. This research extends a well-established glycolysis model, originally formulated as a system of ordinary differential equations (ODEs) into a reaction-diffusion system described by PDEs. The study introduces and analyzes a nonlinear system of two PDEs representing autocatalytic glycolysis with spatial diffusion. Homogeneous Neumann boundary conditions are applied, and a discretization method approximates the system. The goal is to achieve finite-time stability and synchronization of the discrete glycolysis model. Finite-time stability ensures that the concentrations within the system converge to equilibrium within a finite period, providing rapid and precise control over the system’s behavior. The concept of finite-time synchronization is also explored, aiming for all system components to achieve synchronization within a defined time frame. The research includes stability analysis using Lyapunov functions, eigenvalue theory, and finite-time stability theorems, providing a comprehensive approach to understanding and controlling the dynamics of the glycolysis reaction-diffusion system.</p>