# Pinning adaptive anti-synchronization between two general complex dynamical networks with non-delayed and delayed coupling

@article{Wu2012PinningAA, title={Pinning adaptive anti-synchronization between two general complex dynamical networks with non-delayed and delayed coupling}, author={Yongqing Wu and C. Li and Aili Yang and Lunji Song and Yujiang Wu}, journal={Appl. Math. Comput.}, year={2012}, volume={218}, pages={7445-7452} }

Abstract This paper investigates the anti-synchronization (AS) problem of two general complex dynamical networks with non-delayed and delayed coupling using pinning adaptive control method. Based on Lyapunov stability theory and Barbalat lemma, a sufficient condition is derived to guarantee the AS between two networks with non-delayed and delayed coupling. Numerical simulations are also presented to show the effectiveness of the proposed AS criterion.

#### 45 Citations

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Based on the linear negative feedback control scheme, the Lyapunov stability theorem and linear matrix inequality are used to obtain sufficient conditions which guarantee the realization of the cluster synchronization pattern for all initial values. Expand

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A new hybrid synchronization scheme for two different delayed dynamical networks with nonidentical topologies and mixed coupling based on Barbalat lemma and Schur complement lemma is studied, achieving some hybrid synchronization criteria via the open-loop-plus-pinning adaptive control strategy. Expand

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It is shown that the model and results in the paper are more general than those in the literature and some novel and useful synchronisation criteria are presented by adding linear error feedback controllers to certain selected nodes. Expand

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Two theorems on the anti-synchronization based on the Lyapunov stability theory are derived and verified by extensive numerical examples. Expand

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By adding adaptive feedback controllers to a small fraction of network nodes, a low-dimensional pinning sufficient condition is obtained, which can guarantee that the network asymptotically synchronizes to a homogenous trajectory in mean square sense. Expand

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