General Methods to Synchronize Fractional Discrete Reaction–Diffusion Systems Applied to the Glycolysis Model
Tareq Hamadneh, Amel Hioual, Rania Saadeh, Mohamed A. Abdoon, D. K. Almutairi, Thwiba A. Khalid, Adel Ouannas
Abstract
Because they are useful for both enabling numerical simulations and containing well-defined physical phenomena, discrete fractional reaction–diffusion models have attracted a great deal of interest from academics. Within the family of fractional reaction–diffusion models, a discrete form is examined in detail in this study. Furthermore, we investigate the complex synchronization dynamics of a suggested discrete master–slave reaction–diffusion system using the accuracy of linear control techniques combined with a fractional discrete Lyapunov approach. This study’s deviation from the behavior of equivalents with integer orders makes it very fascinating. Like the non-local nature inherent in Caputo fractional derivatives, it creates a memory Lyapunov function that is closely linked to the historical background of the system. The investigation provides a strong basis to the theoretical results.