Pinning a complex dynamical network with time-varying delays

The main contribution of this paper is to propose a method for analyzing pinning stability in a directed complex dynamical network with time-varying delays. Some simple yet generic conditions for pinning such directionally coupling network are derived analytically. It is shown that the controllers could pin a given directed coupling network to a expected homogenous solution, including an equilibrium state, a periodic orbit, or even a chaotic orbit. Subsequently, the obtained results are displayed by a typical scale-free (SF) neuronal network.