Stability and synchronization of memristor-based coupling neural networks with time-varying delays via intermittent control

Generalized intermittent control and its adaptive strategy on stabilization and synchronization of chaotic systems

“…Compared with the traditional periodic intermittent control [13][14][15][16][17][18][21][22][23][24][25][26][27][28][29][30][31][32][33] , the designed control protocols in this paper are more general and more practical. Moreover, to establish the main criteria, comparison principle, the method of piecewise auxiliary function, piecewise analysis technique and the theory of series are applied, which are different from the methods used in [34][35][36] .…”

“…To stabilize the origin, let θ = 1 , T = 5 and the intervals of control time [ t k , δ k ] are defined successively by [0, 2], [4,5], [9,10], [13,15], [17,18], [22, 24.2], [26.5, 28], [31.5, 32.5], [34, 35.5] If the above generalized adaptive intermittent control is reduced to the periodic case, that is, for all k ∈ Z + , t k +1 − t k = T = 5 and δ k − t k = θ = 1 , by Corollary 2 , the origin of system (31) …”

“…8 and d i (0) = 0 for i = 1 , 2 , 3 and θ = 1 , T = 5 . From Theorem 4 , system (32) and system (33) are synchronized under the adaptive intermittent control rules (28) [4,5], [9,10], [13,15], [17,18], [22, 24.2], [26.5, 28], [31.5, 32.5], [34, 35.5] …”

“…Compared with impulsive control, intermittent control is easier to be implemented due to it has a nonzero duration called control time. Recently, a periodic case, called periodically intermittent control, has been successfully applied to stabilize and synchronize neural networks [13][14][15][16][17][18][19][20] , complex networks [21][22][23][24][25] , chaotic systems [26][27][28][29][30][31] . To cut down control gains, Liu and Chen [32] proposed a centralized adaptive intermittent periodically control and some criteria based on rigorously theoretical analysis were provided to guarantee cluster synchronization of complex networks.…”

Pinning synchronization of complex delayed dynamical networks via generalized intermittent adaptive control strategy

“…Compared with impulsive control, intermittent control is easier to be implemented because it may be more reasonable to achieve control process in some time intervals other than some time instants in real control application. The intermittent controller has been successfully applied to stabilize and synchronize neural networks, 21,22 complex networks, [13][14][15][16][23][24][25] and chaotic systems 9,26 in recent decades. Nevertheless, periodic intermittent control may be inadequate in the practical application and may cause unreasonable and unnecessary results.…”