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This paper mainly investigates the projective and lag synchronization between general complex networks via impulsive control. A general drive complex network and an impulsively controlled slave network are presented in the model. Specially, the coupling matrix in this model is not assumed to be symmetric, diffusive or irreducible. Some criteria and corollaries are, respectively, derived for the projective synchronization and lag synchronization between the presented impulsively controlled complex networks. Finally, the results are illustrated by complex networks composed of the chaotic Lorenz systems. All the numerical simulations verify the correctness of the theoretical results.

This paper addresses optimal pinning control of general complex dynamical networks. A pinning scheme with linear feedback is proposed to globally exponentially stabilize a network onto a homogeneous state. In particular, we answer an important and fundamental question about pinning control: how to select an optimal combination between the number of pinned nodes and the feedback control gain? Three illustrative examples are provided to show the effectiveness of the proposed technique.

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