Premium
Global synchronization of fractional‐order and integer‐order N component reaction diffusion systems: Application to biochemical models
Author(s) -
Mesdoui Fatiha,
Shawagfeh Nabil,
Ouannas Adel
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6807
Subject(s) - mathematics , integer (computer science) , reaction–diffusion system , nonlinear system , order (exchange) , synchronization (alternating current) , homotopy analysis method , component (thermodynamics) , fractional calculus , homotopy , mathematical optimization , mathematical analysis , pure mathematics , topology (electrical circuits) , combinatorics , computer science , physics , finance , quantum mechanics , economics , thermodynamics , programming language
This study considers the problem of control and synchronization between fractional‐order and integer‐order, N ‐components reaction‐diffusion systems with nonidentical coefficients and different nonlinear parts. The control scheme is designed using the Lyapunov direct method. The results are exemplified by two significant biochemical models, namely, the fractional‐order Lengyel‐Epstein model and the Gray‐Scott model. To illustrate the effectiveness of the proposed scheme, numerical simulations are performed in one and two space dimensions using Homotopy Analysis Method (HAM).