Global chaos synchronization of new chaotic system using linear active control

Abstract

Chaos synchronization is a procedure where one chaotic oscillator is forced to adjust the properties of another chaotic oscillator for all future states. This research paper studies and investigates the global chaos synchronization problem of two identical chaotic systems and two non‐identical chaotic systems using the linear active control technique. Based on the Lyapunov stability theory and using the linear active control technique, the stabilizing controllers are designed for asymptotically global stability of the closed‐loop system for both identical and non‐identical synchronization. Numerical simulations and graphs are imparted to justify the efficiency and effectiveness of the proposed scheme. All simulations have been done by using mathematica 9. © 2014 Wiley Periodicals, Inc. Complexity 21: 379–386, 2015

Chaos Control and Synchronization of a Novel Chaotic System Based upon Adaptive Control Algorithm

“…For this numerical simulation, the parameters for the new chaotic system [18] (8,21,17) and (15,7,6).…”

“…Chaos Synchronization is one of the critical issues and has received a considerable interest among researchers in nonlinear sciences for more than two decades [6,7] after the exceptional work of Pecorra and Carroll [5]. Until now, certain linear and nonlinear techniques have been proposed and applied successfully to achieve control and synchronization of chaotic systems [8][9][10][11][12][13][14][15][16][17][18][19][20]. Notable among those, ACTs is one of the effectual techniques for stabilizing and synchronizing chaotic systems [11][12][13][14].…”

Chaos control of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity

“…The prominent characteristic of a chaotic system is its extreme sensitivity to initial conditions and the system's parameters. Over the past decades, chaos control has been widely investigated and many researches have been studied in this field [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In [1], a linear feedback control method is proposed for controlling uncertain L€ u system.…”

“…In [8], a nonfragile controller is developed for the problem of exponential synchronization for fractional-order chaotic systems. In [9], a linear active control technique is developed for the global chaos synchronization problem of two identical chaotic systems and two nonidentical chaotic systems. However, these methods [1][2][3][4][5][6][7][8][9] can not deal with the effects caused by input dead-zone nonlinearity and timedelays.…”

“…In [9], a linear active control technique is developed for the global chaos synchronization problem of two identical chaotic systems and two nonidentical chaotic systems. However, these methods [1][2][3][4][5][6][7][8][9] can not deal with the effects caused by input dead-zone nonlinearity and timedelays. In practice, the problem of input dead-zone nonlinearity and time-delays is often encountered in various engineering systems, and the existence of input dead-zone nonlinearity and time-delays frequently becomes a source of instability and poor performance.…”