A New Investigation on Dynamics of the Fractional Lengyel-Epstein Model: Finite Time Stability and Finite Time Synchronization
Hani Almimi, Ma’mon Abu Hammad, Ghadeer Farraj, Issam Bendib, Adel Ouannas
Abstract
In this paper, we present an investigation into the stability of equilibrium points and synchronization within a finite time frame for fractional-order Lengyel–Epstein reaction-diffusion systems. Initially, we utilize Lyapunov theory and multiple criteria to examine the finite-time stability of equilibrium points. Following this analysis, we design efficient, interdependent linear controllers. By applying a Lyapunov function, we define new adequate conditions to ensure finite-time synchronization within a specified time interval. Finally, we provide two illustrative examples to demonstrate the effectiveness and practicality of our proposed method and validate the theoretical outcomes.