Projective synchronization in drive-response dynamical networks

Adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling

“…, N, then the projective synchronization of the drive-response delayed network (2) is achieved, where α is a desired scaling factor. In [24][25][26][27], the authors investigated the projective synchronization of the drive-response dynamical network model, but the time-varying coupling was not considered. The aim of this paper is to discuss the adaptive-impulsive control of projective synchronization in the drive-response delayed complex dynamical networks with time-varying coupling.…”

“…Among all kinds of synchronization, projective synchronization which was first studied in two coupled partially linear systems by Mainer and Reface [20], is one of the most noticeable problems because of its proportionality between the synchronized dynamical states with a scaling factor. Later, the projective synchronization has been extremely investigated in recent years, including chaotic systems [21][22][23] and complex dynamical networks [12,[24][25][26][27]. Hu et al [24] discussed the projective synchronization of a drive-response dynamical network model via pinning control.…”

“…Later, the projective synchronization has been extremely investigated in recent years, including chaotic systems [21][22][23] and complex dynamical networks [12,[24][25][26][27]. Hu et al [24] discussed the projective synchronization of a drive-response dynamical network model via pinning control. Guo et al [25] investigated the projective synchronization in driveresponse networks via impulsive control.…”

Revealing network topology and dynamical parameters in delay-coupled complex network subjected to random noise

“…In the literature, some effective control methods have been reported to realize or enhance synchronization of element dynamics either inside a network or between coupled networks, such as linear or nonlinear feedback control, adaptive control, open-plus-close-loop control, pinning control and impulsive control [4][5][6][7][8][9][10][11][12]. Meanwhile, various kinds of synchronization, including complete synchronization, generalized synchronization, adaptive synchronization, lag synchronization and projective synchronization have been frequently emerged [7][8][9][10][11][12][13][14]. It is worth noting that most of the mentioned works are based on an assumption that the dynamical parameters and topological structures in the networks are exactly known or certain in advance.…”

Projective synchronization between two different time-delayed chaotic systems using active control approach

“…In applications to secure communications, this feature can be used to extend binary digital to M-nary digital communication [6] for achieving fast communication. Projective synchronization of identical chaotic systems has been extremely investigated in recent years, including finite dimensional systems [4,[7][8][9], infinite dimensional systems [10][11][12], and complex networks [13,14]. But in practical situations, it is hardly the case that every component can be assumed to be identical.…”