Synchronization of a Novel Hyperchaotic Complex-Variable System Based on Finite-Time Stability Theory

Abstract

In this paper, we investigate the finite-time synchronization problem of a novel hyperchaotic complex-variable system which generates 2-, 3-and 4-scroll attractors. Based on the finite-time stability theory, two control strategies are proposed to realize synchronization of the novel hyperchaotic complex-variable system in finite time. Finally, two numerical examples have been provided to illustrate the effectiveness of the theoretical analysis.

Fixed-Time Complex Modified Function Projective Lag Synchronization of Chaotic (Hyperchaotic) Complex Systems

“…For instance, Gibbon and McGuinness [1] presented a complex set of Lorenz equations derived in laser optics and baroclinic instability, Zhang and Liu [2] applied synchronization to communication problem under considering time delay, and Wu et al [3] proposed a method to improve the secure communications via passive synchronization of hyperchaotic complex systems. In the literature, researchers have introduced several types of synchronization of chaotic (hyperchaotic) complex systems such as complete synchronization (CoS) [4], antisynchronization (AS) [5], compound synchronization [6], projective synchronization (PS) [7], modified projective and modified function projective synchronization (MPS-MFPS) [8], combinationcombination synchronization [9], complete lag synchronization (CoLS) [10], general hybrid projective complete dislocated synchronization [11], modified projective lag synchronization (MPLS) [12], and modified function projective lag synchronization (MFPLS) [13]. Recently, some new types of synchronization that utilized complex scaling factors have been introduced to achieve the synchronization of both module and phase, the concept first proposed by Nian et al [14].…”

“…In order to obtain such complex synchronization of chaotic (hyperchaotic) complex systems, some control methods such as Lyapunov-based control, feedback control and/or adaptive control [2,5,6,8,[11][12][13][14][15][17][18][19][20], passive control [3], finite-time stability theory-based control [4,9,16], nonlinear observer-based control [7], backstepping-based control [10], and adaptive fuzzy logic control [21] have been proposed. In the mentioned methods, while the ones in [4,9,16] ensure obtaining finite-time synchronization in which the convergence time still depends on both control design parameters 2 Complexity and initial conditions, these remainders guarantee that the synchronization errors might converge to origin asymptotically in the best case.…”

“…In the mentioned methods, while the ones in [4,9,16] ensure obtaining finite-time synchronization in which the convergence time still depends on both control design parameters 2 Complexity and initial conditions, these remainders guarantee that the synchronization errors might converge to origin asymptotically in the best case. It is certain that synchronization errors could reach to zero in an amount of time which is more desirable object.…”

Combination-Combination Synchronization of Four Nonlinear Complex Chaotic Systems

“…Based on the passive theory, the authors studied the projective synchronization of hyperchaotic complex nonlinear systems and its application in secure communications [17]. In [18], the authors achieved fast synchronization of a novel hyperchaotic complex system based on finite-time stability theory.…”

Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

“…Furthermore the synchronization error system between the coupled chaotic systems may be asymptotically stable if some suitable control techniques are implemented on them. As a common multi-disciplinary phenomenon, chaos synchronization has broad range applications, such as secure communication [1], OPEN ACCESS chaotic economic systems [2], WINDMI systems [3], hyperchaotic complex-variable systems [4], chaotic complex networks [5], fractional-order chaotic neural networks [6], etc.…”