Full-commanding a network: The dictator

A network of chaotic dynamical systems may synchronize. For some networks there is the possibility that, coupling a new node to the network, the synchronization will be commanded by that new node. That possibility depends on the network and on the way the new node is coupled to the network.We consider a coupling that can provide what we call a full-commanding and we define the corresponding full-commandwindow. The limit situations corresponding to a completely connected network and to a completely disconnected one provide us some understanding about what makes a network more receptive or more resistant to commanding