Global Stability Analysis of Fractional Selkov-Schnakenberg Reaction-Diffusion Systems

Iqbal H. Jebril; Issam Bendib; Adel Ouannas; Salah Boulaaras; Iqbal M. Batiha; Shaher Momani

doi:10.1007/978-3-031-95381-1_3

Global Stability Analysis of Fractional Selkov-Schnakenberg Reaction-Diffusion Systems

Iqbal H. Jebril
, Issam Bendib
, Adel Ouannas
, Salah Boulaaras
, Iqbal M. Batiha
, Shaher Momani

Nonlinear Dynamic Research Centre (NDRC)

Al-Zaytoonah University of Jordan
Frères Mentouri Constantine 1 University
University of Oum El Bouaghi
Qassim University
University of Jordan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This study investigates the global stability of fractional-order (FO) Selkov-Schnakenberg (SS) reaction-diffusion systems (RDs), which are pivotal in modeling biochemical oscillations and pattern formation in chemical systems. By extending the Lyapunov function (LF) method, sufficient conditions for the global asymptotic stability (GAS) of the system’s unique equilibrium point (EP) are derived. Numerical simulations validate the theoretical findings and reveal insights into the dynamic behavior of the FOSSRDs under various fractional orders and parameter settings. The results contribute to understanding complex RD dynamics and their implications in biochemical processes.

Original language	English
Title of host publication	Fractional Calculus and Applications, ICFCA 2024
Editors	Omar Naifar, Abdellatif Ben Makhlouf, Abdellatif Ben Makhlouf, Mohamed Ali Hammami
Publisher	Springer
Pages	41-55
Number of pages	15
ISBN (Print)	9783031953804
DOIs	https://doi.org/10.1007/978-3-031-95381-1_3
State	Published - 2025
Event	International Conference on Fractional Calculus and Applications, ICFCA 2024 - Sousse, Tunisia Duration: 26 Dec 2024 → 30 Dec 2024

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	505
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Fractional Calculus and Applications, ICFCA 2024
Country/Territory	Tunisia
City	Sousse
Period	26/12/24 → 30/12/24

Keywords

Fractional-order systems
Global asymptotic stability
Lyapunov function
Selkov-Schnakenberg model

Access to Document

10.1007/978-3-031-95381-1_3

Cite this

Jebril, I. H., Bendib, I., Ouannas, A., Boulaaras, S., Batiha, I. M., & Momani, S. (2025). Global Stability Analysis of Fractional Selkov-Schnakenberg Reaction-Diffusion Systems. In O. Naifar, A. Ben Makhlouf, A. Ben Makhlouf, & M. A. Hammami (Eds.), Fractional Calculus and Applications, ICFCA 2024 (pp. 41-55). (Springer Proceedings in Mathematics and Statistics; Vol. 505). Springer. https://doi.org/10.1007/978-3-031-95381-1_3

Jebril, Iqbal H. ; Bendib, Issam ; Ouannas, Adel et al. / Global Stability Analysis of Fractional Selkov-Schnakenberg Reaction-Diffusion Systems. Fractional Calculus and Applications, ICFCA 2024. editor / Omar Naifar ; Abdellatif Ben Makhlouf ; Abdellatif Ben Makhlouf ; Mohamed Ali Hammami. Springer, 2025. pp. 41-55 (Springer Proceedings in Mathematics and Statistics).

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title = "Global Stability Analysis of Fractional Selkov-Schnakenberg Reaction-Diffusion Systems",

abstract = "This study investigates the global stability of fractional-order (FO) Selkov-Schnakenberg (SS) reaction-diffusion systems (RDs), which are pivotal in modeling biochemical oscillations and pattern formation in chemical systems. By extending the Lyapunov function (LF) method, sufficient conditions for the global asymptotic stability (GAS) of the system{\textquoteright}s unique equilibrium point (EP) are derived. Numerical simulations validate the theoretical findings and reveal insights into the dynamic behavior of the FOSSRDs under various fractional orders and parameter settings. The results contribute to understanding complex RD dynamics and their implications in biochemical processes.",

keywords = "Fractional-order systems, Global asymptotic stability, Lyapunov function, Selkov-Schnakenberg model",

author = "Jebril, \{Iqbal H.\} and Issam Bendib and Adel Ouannas and Salah Boulaaras and Batiha, \{Iqbal M.\} and Shaher Momani",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.; International Conference on Fractional Calculus and Applications, ICFCA 2024 ; Conference date: 26-12-2024 Through 30-12-2024",

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doi = "10.1007/978-3-031-95381-1\_3",

language = "English",

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series = "Springer Proceedings in Mathematics and Statistics",

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pages = "41--55",

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}

Jebril, IH, Bendib, I, Ouannas, A, Boulaaras, S, Batiha, IM & Momani, S 2025, Global Stability Analysis of Fractional Selkov-Schnakenberg Reaction-Diffusion Systems. in O Naifar, A Ben Makhlouf, A Ben Makhlouf & MA Hammami (eds), Fractional Calculus and Applications, ICFCA 2024. Springer Proceedings in Mathematics and Statistics, vol. 505, Springer, pp. 41-55, International Conference on Fractional Calculus and Applications, ICFCA 2024, Sousse, Tunisia, 26/12/24. https://doi.org/10.1007/978-3-031-95381-1_3

Global Stability Analysis of Fractional Selkov-Schnakenberg Reaction-Diffusion Systems. / Jebril, Iqbal H.; Bendib, Issam; Ouannas, Adel et al.
Fractional Calculus and Applications, ICFCA 2024. ed. / Omar Naifar; Abdellatif Ben Makhlouf; Abdellatif Ben Makhlouf; Mohamed Ali Hammami. Springer, 2025. p. 41-55 (Springer Proceedings in Mathematics and Statistics; Vol. 505).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Global Stability Analysis of Fractional Selkov-Schnakenberg Reaction-Diffusion Systems

AU - Jebril, Iqbal H.

AU - Bendib, Issam

AU - Ouannas, Adel

AU - Boulaaras, Salah

AU - Batiha, Iqbal M.

AU - Momani, Shaher

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

PY - 2025

Y1 - 2025

N2 - This study investigates the global stability of fractional-order (FO) Selkov-Schnakenberg (SS) reaction-diffusion systems (RDs), which are pivotal in modeling biochemical oscillations and pattern formation in chemical systems. By extending the Lyapunov function (LF) method, sufficient conditions for the global asymptotic stability (GAS) of the system’s unique equilibrium point (EP) are derived. Numerical simulations validate the theoretical findings and reveal insights into the dynamic behavior of the FOSSRDs under various fractional orders and parameter settings. The results contribute to understanding complex RD dynamics and their implications in biochemical processes.

AB - This study investigates the global stability of fractional-order (FO) Selkov-Schnakenberg (SS) reaction-diffusion systems (RDs), which are pivotal in modeling biochemical oscillations and pattern formation in chemical systems. By extending the Lyapunov function (LF) method, sufficient conditions for the global asymptotic stability (GAS) of the system’s unique equilibrium point (EP) are derived. Numerical simulations validate the theoretical findings and reveal insights into the dynamic behavior of the FOSSRDs under various fractional orders and parameter settings. The results contribute to understanding complex RD dynamics and their implications in biochemical processes.

KW - Fractional-order systems

KW - Global asymptotic stability

KW - Lyapunov function

KW - Selkov-Schnakenberg model

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DO - 10.1007/978-3-031-95381-1_3

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AN - SCOPUS:105021006071

SN - 9783031953804

T3 - Springer Proceedings in Mathematics and Statistics

SP - 41

EP - 55

BT - Fractional Calculus and Applications, ICFCA 2024

A2 - Naifar, Omar

A2 - Ben Makhlouf, Abdellatif

A2 - Hammami, Mohamed Ali

PB - Springer

T2 - International Conference on Fractional Calculus and Applications, ICFCA 2024

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Jebril IH, Bendib I, Ouannas A, Boulaaras S, Batiha IM , Momani S. Global Stability Analysis of Fractional Selkov-Schnakenberg Reaction-Diffusion Systems. In Naifar O, Ben Makhlouf A, Ben Makhlouf A, Hammami MA, editors, Fractional Calculus and Applications, ICFCA 2024. Springer. 2025. p. 41-55. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-031-95381-1_3