Stability Analysis of a Fractional-Order Lengyel–Epstein Chemical Reaction Model
(1) Khelifa Bouaziz Mail (Larbi Tebessi University, Algeria)
(2) Nadhir Djeddi Mail (Larbi Tebessi University, Algeria)
(3) Osama Ogilat Mail (Al-Ahliyya Amman University, Jordan)
(4) * Iqbal M. Batiha Mail (1) Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan. 2) Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE)
(5) Nidal Anakira Mail (Sohar University, Oman)
(6) Tala Sasa Mail (Applied Science Private University, Jordan)
*corresponding author

Abstract


In this paper, we stady a mathematical model based on a system of fractional-order differential equations to describe the dynamics of the Lengyel–Epstein chemical reaction, which is well known for exhibiting oscillatory behavior. The use of fractional derivatives allows in chemical processes compared to classical integer-order models. We specifically focus on analyzing the stability of the system’s positive equilibrium point by applying fractional calculus techniques. The stability conditions are derived and discussed in the context of the fractional-order parameters. To validate the theoretical findings, we perform numerical simulations using the Forward Euler method adapted for fractional-order systems. These simulations illustrate the impact of the fractional order on the system’s dynamic behavior and confirm the analytical results regarding equilibrium stability.


Keywords


Lengyel-Epstein Chemical; Oscillatory Chemical Reactions; Stability Analysis; Equilibrium Points; Numerical Simulation; Forward Euler Method

   

DOI

https://doi.org/10.31763/ijrcs.v5i2.1848 		      

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