A novel criterion for cluster synchronization of complex dynamical networks with coupling time-varying delays

Impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach

“…Ji, Park, Yoo, Won and Lee, (2010), discussed the synchronization problem for a class of complex dynamical networks in which every identical node is a Lur'e system with time-varying delay. Wang, Yao, Zheng and Xie, (2012), investigated the cluster synchronization problem for the time-varying delays coupling networks with nonidentical delayed dynamical systems by using the pinning control method. Yang and Cao, (2010), deal with the stability analysis of the impulsive functional differential equation and the exponential synchronization of the complex dynamical network with a coupling delay and impulses.…”

Cluster synchronization in complex networks of nonidentical dynamical systems via pinning control

“…That is to say, if we want the nodes finally converge to some targets, the external control should be added. Moreover, for constant coupling strength, the cluster synchronization may not be realized, while by adding external control, the cluster synchronization can be achieved, see [40][41][42]. However, all these works realize the synchronization by adding the controllers on all clusters, that is to say, any cluster should be finally synchronized to these given targets.…”

Synchronization for non-dissipatively coupled time-varying complex dynamical networks with delayed coupling nodes

“…Thus, synchronization of complex dynamical networks has been investigated extensively . Many kinds of synchronization, such as exponential synchronization [11], asymptotic synchronization [21], finite-time synchronization [9], cluster synchronization [23,24], have been discussed.…”

“…In reality, many realist networks, particularly biological networks such as flocks of birds and schools of fishes, are with time-varying coupling structures [4,27]. Therefore, it is also very necessary to investigate the synchronization problem for timevarying networks, and some synchronization criteria have been proposed [22][23][24][25][26][27][28][29][30]. For example, [27] firstly introduced a time-varying complex dynamical network model and then investigated its synchronization phenomenon.…”

“…[22][23][24] proposed different synchronization criteria for the networks with time-varying coupling strength. However, it should be noted that all the synchronization schemes in [22][23][24][25][26][27][28][29][30] are only valid for the dissipatively coupled networks and their outer coupling coefficients should be exactly known in advance. Therefore, we should further investigate the synchronization of the networks with non-dissipatively coupled nodes and unknown time-varying couplings.…”