On the asymptotic stability of the time--fractional Lengyel--Epstein system
Djamel Mansouri, Salem Abdelmalek, Samir Bendoukha
TL;DR
This paper investigates the stability of a time-fractional version of the Lengyel--Epstein reaction model, establishing conditions for equilibrium stability and illustrating how fractional order influences system behavior.
Contribution
It introduces a fractional calculus approach to the Lengyel--Epstein model and derives new stability conditions for the fractional system.
Findings
Invariant regions are defined for the fractional system.
Sufficient conditions for local and global stability are established.
Numerical simulations show the impact of fractional order on dynamics.
Abstract
This paper concerns a time fractional version of the conventional Lengyel--Epstein CIMA reaction model. We define the invariant regions of the system and establish sufficient conditions for the unique equilibrium's local and global asymptotic stability. Numerical results are presented to illustrate the effect of the fractional order on system dynamics.
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