Adaptive Synchronization and Antisynchronization of a Hyperchaotic Complex Chen System with Unknown Parameters Based on Passive Control

Abstract

This paper investigates the synchronization and antisynchronization problems of a hyperchaotic complex Chen system with unknown parameters based on the properties of a passive system. The essential conditions are derived under which the synchronization or antisynchronization error dynamical system could be equivalent to a passive system and be globally asymptotically stabilized at a zero equilibrium point via smooth state feedback. Corresponding parameter estimation update laws are obtained to estimate the unknown parameters as well. Numerical simulations verify the effectiveness of the theoretical analysis.

Analytical and Numerical Study of the Projective Synchronization of the Chaotic Complex Nonlinear Systems with Uncertain Parameters and Its Applications in Secure Communication

“…In Figure 4 it can be seen that the synchronization errors will converge to zero after small value of . Figure 4 shows the estimations of̃( ),̃( ),̃( ),̃( ),]( ), and̃( ) of the unknown parameters of master and slave systems (20) and (21) which converge to = 14, = 35, = 3.7, = 40, ] = 22, and = 5, respectively, as → ∞.…”

“…Many researchers had shown the possibility to achieve projective synchronization between two chaotic systems (with real variables) with known or unknown parameters [3][4][5][6]. There also exist, however, interesting cases of dynamical systems, where the main variables participating in the dynamics are complex [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. The projective synchronization of two identical chaotic complex systems with certain parameters is investigated in [26].…”

Adaptive Synchronization Strategy between Two Autonomous Dissipative Chaotic Systems Using Fractional-Order Mittag–Leffler Stability

“…So, these systems have a very broad range of potential applications in the field of secure communication and other related sciences where chaotic synchronization is the key technology. Scholars in nonlinear control disciplines have proposed a number of effective synchronization methods since the pioneering work of Pecora and Carroll in 1996 [24], including drive-response synchronization [25], active-passive synchronization [26], coupled synchronization [27], continuous variable feedback synchronization [28], adaptive synchronization [29][30][31][32][33], pulse synchronization [34], projection synchronization [35], finite time synchronization [36], sliding mode control synchronization [37], hybrid synchronization [38,39], and other methods [40][41][42]. Chaotic synchronization is a kind of chaos control technology.…”

Adaptive generalized combination complex synchronization of uncertain real and complex nonlinear systems

“…Compared to chaotic real systems, chaotic complex systems exhibit more abundant and complicated dynamical behaviors with strong unpredictability, which can be applied to chaos secure communication for the sake of higher signal transmission efficiency and secure performance. [2][3][4] Therefore, much attention and many efforts are devoted to investigate synchronization of chaotic complex systems in recent years, and various synchronization schemes have been proposed and realized successfully, such as complete synchronization, 5,6 antisynchronization, 7,8 lag synchronization, 9,10 phase synchronization, 11 projective synchronization, 12,13 and their extended synchronization schemes. [14][15][16][17][18][19] All of the above-mentioned synchronization methods are designed for one drive system and one response system.…”