International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3642 2020 2020 Department of Mathematics, Faculty of Science and Information Technology, Jadara University, P.O. Box 733, Irbid 21110, Jordan Rania Rania Applied Mathematics and Modeling Laboratory, Department of Mathematics, Faculty of Exact Sciences, Brothers Mentouri University of Constantine, Algeria Issam Bendib Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan Ahmad Qazza rsaadeh@zu.edu.jo Rania Saadeh Department of Mathematics and Computer Science , University of Oum EL-Bouaghi, Oum El Bouaghi 04000, Algeria Adel Ouannas Applied Mathematics and Modeling Laboratory, Department of Mathematics, Faculty of Exact Sciences, Brothers Mentouri University of Constantine, Algeria Mohamed Dalah 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 2025 371 386 10.54216/IJNS.250431 https://www.americaspg.com/articleinfo/21/show/3642