Research Article Synchronization Control in Reaction-Diffusion Systems: Application to Lengyel-Epstein System Adel Ouannas, 1 Mouna Abdelli, 1 Zaid Odibat, 2,3 Xiong Wang , 4 Viet-Thanh Pham , 5,6 Giuseppe Grassi, 7 and Ahmed Alsaedi 3  Department of Mathematics, University of Larbi Tebessi, Tebessa , Algeria  Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt , Jordan  Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah , Saudi Arabia  Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong , China  Faculty of Electrical and Electronic Engineering, Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong district, Hanoi , Vietnam  Phenikaa Research and Technology Institute (PRATI), A&A Green Phoenix Group,  Hoang Ngan, Hanoi , Vietnam  Universita del Salento, Dipartimento Ingegneria Innovazione,  Lecce, Italy Correspondence should be addressed to Viet-anh Pham; thanh.phamviet@phenikaa-uni.edu.vn Received 29 October 2018; Revised 4 January 2019; Accepted 10 February 2019; Published 24 February 2019 Guest Editor: Baltazar Aguirre-Hernandez Copyright © 2019 Adel Ouannas et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Synchronization and control in high dimensional spatial-temporal systems have received increasing interest in recent years. In this paper, the problem of complete synchronization for reaction-diffusion systems is investigated. Linear and nonlinear synchronization control schemes have been proposed to exhibit synchronization between coupled reaction-diffusion systems. Synchronization behaviors of coupled Lengyel-Epstein systems are obtained to demonstrate the effectiveness and feasibility of the proposed control techniques. 1. Introduction Synchronization of chaos is a phenomenon that may occur when two, or more, chaotic systems adjust a given property of their motion to a common behavior due to a coupling or to a forcing. is phenomenon has attracted the interest of many researchers from various fields due to its potential applications in physics, biology, chemistry, and engineering sciences since the pioneering work by Pecora and Carroll [1]. Various synchronization types have been presented, such as complete synchronization, phase synchronization, lag synchronization, anticipated synchronization, function projective synchronization, generalized synchronization, and Q-S synchronization. Most of the research efforts have been devoted to the study of chaos control and chaos synchronization problems in low-dimensional nonlinear dynamical systems [2–10]. Syn- chronizing high dimensional systems in which state variables depend not only on time but also on the spatial position remains a challenge. ese high dimensional systems are generally modelled in spatial-temporal domain by partial differential systems. Recently, the search for synchroniza- tion has moved to high dimensional nonlinear dynamical systems. Over the last years, some studies have investigated synchronization of spatially extended systems demonstrating spatiotemporal chaos such as the work presented in [11–32]. Synchronization dynamics of reaction-diffusion systems has been studied in [11, 12] using phase reduction theory. It has been shown that reaction-diffusion systems can exhibit syn- chronization in a similar way to low-dimensional oscillators. A general approach for synchronizing coupled partial differ- ential equations with spatiotemporally chaotic dynamics by driving the response system only at a finite number of space points has been introduced in [13, 14]. Synchronization and control for spatially extended systems based on local spatially averaged coupling signals have been presented in [17]. e Hindawi Complexity Volume 2019, Article ID 2832781, 8 pages https://doi.org/10.1155/2019/2832781