A Comprehensive Analysis on Controlling and Hybrid Synchronization in Identical Chaotic Systems via Active Control Method

Abstract

The current research provides the potential role of active nonlinear control functions in the asymptotic convergence of the synchronized errors in a comprehensive manner. Firstly, we design a systematic procedure to investigate hybrid synchronization in identical chaotic chemical reactor systems via active control method (ACM). In view of master-slave configuration and Lyapunov’s theory of stability, the considered methodology determines the global asymptotic stability of the error dynamics of the given system. Finally, numerical simulations using MATLAB toolbox are implemented for illustrating the efficacy and feasibility of the discussed strategy.

Керування Хаосом За Допомогою Зовнішнього Періодичного Примусу В Автокаталітичній Дисипативній Хімічній Системі

“…Controlling chaos is very important in many circumstances from the point of view of preventing disaster and collapse in a dynamical system. In recent years, after the pioneering work of Ott, Grebogi and Yorke (OGY) [8], controlling chaos has become more and more interesting in academic research and practical applications [9][10][11][12][13][14][15][16]. The first control experiment in chemical chaos was carried out in a BZ reaction by the group of Showalter in 1993.…”

Internal Synchronization Using Adaptive Control

“…This is the reason why chaos synchronization has drawn the attention of scholars from all across. Various as well as numerous methods have been presented for synchronization of chaotic systems, such as active control [4][5][6][7], backstepping control [8,9], fuzzy control [10,11], impulsive control [12][13][14], event-triggered-based neural network [15,16], output feedback control [17,18], projective synchronization [19], and sliding mode control [20][21][22]. It is worth mentioning the recent contribution of various synchronization techniques that have been proposed.…”

Chaos Controllability in Fractional-Order Systems via Active Dual Combination–Combination Hybrid Synchronization Strategy

“…hybrid synchronization [22], combination projective synchronization [13], dual combination synchronization (DCS) [23], double compound synchronization [24], combinationdifference synchronization [1], and hybrid projective combination-combination synchronization (CCS) [25]. Dual synchronization is a specialized characteristic of chaos synchronization wherein four identical and non-identical chaotic systems (two masters along with two slave systems) are synchronized.…”