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International Journal of Neutrosophic Science

Volume 26 , Issue 4 , PP: 155-166, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Finite-Time Stability in the Discrete Sel’kov-Schnakenberg Reaction-Diffusion Model: Analytical Analysis and Numerical Simulations

Salam Alnabulsi 1 , Wael Mahmoud Mohammad Salameh 2 , Issam Bendib 3 * , Ahmad A. Abubaker 4 , Adel Ouannas 5 , Abdallah Al-Husban 6

  • 1 Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan - (s.alnabulsi@ju.edu.jo)
  • 2 Faculty of Information Technology, Abu Dhabi University, Abu Dhabi, UAE - (wael.salameh@adu.ac.ae)
  • 3 Laboratory of Applied Mathematics and Modeling, Department of Mathematics, Faculty of Exact Sciences, University of Constantine 1, Constantine 25017, Algeria - (bendib.issam@doc.umc.edu.dz)
  • 4 Faculty of Computer Studies, Arab Open University, Saudi Arabia - (a.abubaker@arabou.edu.sa)
  • 5 Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria - (ouannas.adel@univ-oeb.dz)
  • 6 Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box 2600, Irbid, Jordan; Jadara University Research Center, Jadara University, Jordan - (dralhosban@inu.edu.jo)

    • Doi: https://doi.org/10.54216/IJNS.260415

    Received: February 25, 2025 Revised: March 21, 2025 Accepted: June 04, 2025
    Abstract

    This study investigates the finite-time stability (FTS) of the discrete Sel’kov-Schnakenberg reaction-diffusion (SSRD) system, a mathematical model capturing the interplay between local reactions and spatial diffusion. A novel discretization framework based on finite difference methods (FDM) is developed to transform the continuous reaction-diffusion (RD) system into a discrete counterpart, enabling detailed computational analysis. Sufficient conditions for FTS are derived using Lyapunov functions (LF) and eigenvalue-based methods, ensuring precise predictions of the system’s behavior. Numerical simulations validate theoretical findings, demonstrating the proposed methods’ practical applicability to scenarios such as chemical reactions, biological processes, and technological systems. The influence of system parameters, boundary conditions, and initial conditions on the dynamic behavior is systematically analyzed. This study contributes to the broader understanding of RD systems, addressing key challenges in stability analysis and offering a computationally efficient framework with implications for science and engineering.

    Keywords :

    Finite-time stabilit , Reaction-diffusion systems , Sel&rsquo , kov-Schnakenberg model , Finite difference methods , Lyapunov functions

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    Cite This Article As :
    Alnabulsi, Salam. , Mahmoud, Wael. , Bendib, Issam. , A., Ahmad. , Ouannas, Adel. , Al-Husban, Abdallah. Finite-Time Stability in the Discrete Sel’kov-Schnakenberg Reaction-Diffusion Model: Analytical Analysis and Numerical Simulations. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 155-166. DOI: https://doi.org/10.54216/IJNS.260415
    Alnabulsi, S. Mahmoud, W. Bendib, I. A., A. Ouannas, A. Al-Husban, A. (2025). Finite-Time Stability in the Discrete Sel’kov-Schnakenberg Reaction-Diffusion Model: Analytical Analysis and Numerical Simulations. International Journal of Neutrosophic Science, (), 155-166. DOI: https://doi.org/10.54216/IJNS.260415
    Alnabulsi, Salam. Mahmoud, Wael. Bendib, Issam. A., Ahmad. Ouannas, Adel. Al-Husban, Abdallah. Finite-Time Stability in the Discrete Sel’kov-Schnakenberg Reaction-Diffusion Model: Analytical Analysis and Numerical Simulations. International Journal of Neutrosophic Science , no. (2025): 155-166. DOI: https://doi.org/10.54216/IJNS.260415
    Alnabulsi, S. , Mahmoud, W. , Bendib, I. , A., A. , Ouannas, A. , Al-Husban, A. (2025) . Finite-Time Stability in the Discrete Sel’kov-Schnakenberg Reaction-Diffusion Model: Analytical Analysis and Numerical Simulations. International Journal of Neutrosophic Science , () , 155-166 . DOI: https://doi.org/10.54216/IJNS.260415
    Alnabulsi S. , Mahmoud W. , Bendib I. , A. A. , Ouannas A. , Al-Husban A. [2025]. Finite-Time Stability in the Discrete Sel’kov-Schnakenberg Reaction-Diffusion Model: Analytical Analysis and Numerical Simulations. International Journal of Neutrosophic Science. (): 155-166. DOI: https://doi.org/10.54216/IJNS.260415
    Alnabulsi, S. Mahmoud, W. Bendib, I. A., A. Ouannas, A. Al-Husban, A. "Finite-Time Stability in the Discrete Sel’kov-Schnakenberg Reaction-Diffusion Model: Analytical Analysis and Numerical Simulations," International Journal of Neutrosophic Science, vol. , no. , pp. 155-166, 2025. DOI: https://doi.org/10.54216/IJNS.260415

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