The impulsive control synchronization of the drive-response complex system

Pinning synchronization of weighted complex networks with variable delays and adaptive coupling weights

“…Select μ 12 = μ 13 = 0.01 and μ 14 = μ 15 = 0.02 in the adaptive law (8) and ω 12 (0) = ω 13 (0) = 0.05, ω 14 (0) = ω 15 (0) = 0.03. Itfollows from Corollary 2 that system (17) is synchronized to chaotic system(16), which is verified byFig. 7, and in this case, the coupling weights ω ij and the feedback gains β i respectively converge to some constants that are shown in Figs.8-9.…”

“…. , 5, where A 2 , B 2 , D 2 , h(x i ), τ (t) are defined in system (16), and the configuration matrix C is given by…”

“…Up to now, many different regimes of synchronization have been investigated, including cluster synchronization [3][4][5][6][7], phase synchronization [8], complete synchronization [9][10][11][12], and generalized synchronization [13][14][15]. Meanwhile, many effective control approaches have been developed to synchronize complex networks such as impulsive control [16][17][18], intermittent control [19,20], adaptive feedback control [21][22][23][24][25], and so on.…”

Adaptive bidirectionally coupled synchronization of chaotic systems with unknown parameters

“…A variety of methods and techniques have been proposed for the control and synchronization of chaotic systems. In past years, most synchronizing techniques have been designed for unidirectionally coupled systems, such as the sliding mode control [2,3], observer-based control [4,5], backstepping control [6,7], nonlinear control [8,9], impulsive synchronization [10,11], and so on.…”

Projective and lag synchronization between general complex networks via impulsive control

“…In this period, several different theoretical methods including adaptive synchronization [13,14], robust synchronization [15], pinning control [16][17][18] and impulsive control [19][20][21][22][23] have been introduced to solve the above problem. Among these approaches, it has been shown that the impulsive control method is a more popular method, which is relatively higher efficient and easily realized.…”