Pinning complex dynamical networks to a desired synchronization orbit

In this paper we propose a method for analyzing pinning synchronization stability in a complex dynamical network with directionally coupling. By developing the analysis procedure of pinning stability for directed coupled dynamical networks, some simple yet generic criteria of pinning synchronization for such coupled network are derived analytically. It is shown that in order to make a complex networks drive to a desired synchronization orbit, the coupling strength varies according to the controller. Subsequently, the theoretic results are illustrated by a typical scale-free (SF) network. Numerical simulations are finally given to demonstrate the effectiveness of the proposed control methodology.