Pinning impulsive synchronization in coupled delayed directed dynamical networks

In this brief, the issues of pinning synchronization in a coupled delayed directed dynamical network are investigated via impulsive control, and a simple yet generic criterion of pinning impulsive synchronization for such coupled network is derived analytically. It is shown that a single impulsive controller can always pin a given coupled delayed directed network to a desired homogenous solution. Subsequently, the theoretic results are illustrated by a typical small-world (SW) network composing of the well known Hodgkin-Huxley neuron oscillators. Numerical simulations are finally given to demonstrate the effectiveness of the proposed control methodology.