Full command of a network by a new node: some results and examples

Abstract

We consider that a network of chaotic identical dynamical systems is connected to a new node. Depending on some properties of the network and on the way that connection is made, the new node may control the network. We consider a full-command connection and analyze the possibility of the network being full-commandable by the new node. For full-commandable networks, we define the full-command-window, a set that includes some of the values that the coupling strength of the new node may assume. We present several results and examples that enlight us how a network can become more vulnerable or resistant to full-command.