aspg-21-3642-1791468696 20261008141136 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 4 Raed Hatamleh Department of Mathematics, Faculty of Science and Information Technology, Jadara University, P.O. Box 733, Irbid 21110, Jordan Issam Bendib Applied Mathematics and Modeling Laboratory, Department of Mathematics, Faculty of Exact Sciences, Brothers Mentouri University of Constantine, Algeria Ahmad Qazza Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan Rania Saadeh rsaadeh@zu.edu.jo Adel Ouannas Department of Mathematics and Computer Science , University of Oum EL-Bouaghi, Oum El Bouaghi 04000, Algeria Mohamed Dalah Applied Mathematics and Modeling Laboratory, Department of Mathematics, Faculty of Exact Sciences, Brothers Mentouri University of Constantine, Algeria 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. 2025 371 386 3642 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250431 https://www.americaspg.com/journal/21/article/3642 https://www.americaspg.com/storage/01740423652.pdf