Computation (Sep 2024)

A New Investigation on Dynamics of the Fractional Lengyel-Epstein Model: Finite Time Stability and Finite Time Synchronization

  • Hani Mahmoud Almimi,
  • Ma’mon Abu Hammad,
  • Ghadeer Farraj,
  • Issam Bendib,
  • Adel Ouannas

DOI
https://doi.org/10.3390/computation12100197
Journal volume & issue
Vol. 12, no. 10
p. 197

Abstract

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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.

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