Volume 25 , Issue 4 , PP: 371-386, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Raed Hatamleh 1 , Issam Bendib 2 , Ahmad Qazza 3 , Rania Saadeh 4 * , Adel Ouannas 5 , Mohamed Dalah 6
Doi: https://doi.org/10.54216/IJNS.250431
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.
Finite-time stability , Glycolysis reaction-diffusion system , Lyapunov stability , Finite-time synchronization scheme
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