Finite time Stability and Synchronization of the Glycolysis Reaction-Diffusion model Raed Hatamleh1 , Issam Bendib2 , Ahmad Qazza3 , Rania Saadeh3,∗ , Adel Ouannas4 , Mohamed Dalah2 1Department of Mathematics, Faculty of Science and Information Technology, Jadara University, P.O. Box 733, Irbid 21110, Jordan 2Applied Mathematics and Modeling Laboratory, Department of Mathematics, Faculty of Exact Sciences, Brothers Mentouri University of Constantine, Algeria 3Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan 4Department of Mathematics and Computer Science , University of Oum EL-Bouaghi, Oum El Bouaghi 04000, Algeria Emails: raed@jadara.edu.jo; bendib.issam@doc.umc.edu.dz; aqazza@zu.edu.jo; rsaadeh@zu.edu.jo; ouannas.adel@univ-oeb.dz; dalah.mohamed@umc.edu.dz Abstract Finite-time stability is a critical property for systems where rapid stabilization is required, as it ensures that the system reaches and maintains equilibrium within a specified time frame, regardless of initial conditions. This contrasts with asymptotic stability, which only guarantees eventual convergence over an indefinite period. This research focuses on demonstrating the finite-time stability of the glycolysis reaction-diffusion system at its equilibrium point. The equilibrium points of the system are derived, and finite-time stability conditions are established. Definitions and lemmas are provided to support the theoretical framework, including conditions for finite-time convergence and Lyapunov stability. A key result shows that the system possesses a unique equilibrium point that can achieve finite-time stability under certain conditions. Additionally, the finite-time synchronization scheme is discussed, highlighting the process of rapidly achieving synchronized behavior in reaction-diffusion systems. The proposed method involves associating the main system with a response system and addressing synchronization discrepancies through the introduction of an error vector. This research provides a robust framework for understanding and achieving finite-time stability and synchronization in complex reaction-diffusion systems. Keywords: Finite-time stability; Glycolysis reaction-diffusion system; Lyapunov stability; Finite-time synchronization scheme