Abstract
Pinning adaptive synchronization is investigated in weighted complex networks and several criteria are obtained for globally exponentially asymptotic synchronization. The number of pinned nodes can be obtained by calculating the eigenvalue of the minor matrix of an extended coupling matrix. Especially, pinning adaptive controllers are rather simple compared with some traditional controllers. Specifically and randomly pinning schemes are considered. When the network Control Rank information is known, the specifically pinning scheme of the most highly connected nodes is shown to require a significantly smaller number of local controllers when compared with the randomly pinning scheme. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed synchronization criteria in weighted dynamical networks.
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