Pinning Complex Delayed Dynamical Networks by a Single Impulsive Controller

In this paper, we propose a novel approach for analyzing synchronization stability in a complex delayed dynamical network via impulsive control. We present the sufficiency conditions for pinning synchronization stability of single impulsive controller for an undirected complex delayed dynamical network in the presence of identical coupling delays between nodes. We also show that a single impulsive controller can always pin a given complex delayed dynamical network to a homogenous solution, provided that both the coupling strength and coupling delay are properly selected. Subsequently, the results are illustrated by a typical scale-free (SF) network composing of the representative oscillators and a small-world (SW) neuronal network. Numerical simulations with three kinds of the homogenous solutions, including an equilibrium point, a periodic orbit, and a chaotic orbit, are finally given to demonstrate the effectiveness of the proposed control methodology.