Network controllability based on node overloaded failure

Abstract

Liu and Barabasi applied the modern control theory to the network controllability of linear dynamical systems and proposed a method to calculate the minimal set of driver node which controls the states of all nodes in a linear time invariant complex network with any topology. The network controllability model solves the computable problems of the network controllability. Facing the problem of node overloaded failure in real networks, in the paper we investigate the model of network controllability based on node overloaded failure. Through the simulation of betweenness and Weibull failure model, the results demonstrate that the difficulty in maintaining the controllability of SF network is significantly greater than that of ER network. In the target failure mechanism, even if the failure signals input rarely to the networks, they can greatly increase the difficulty of network controllability. Besides, the node failure based high betweenness centrality is more efficient than failure based high degree on damaging network controllability, which indicates the nodes with high betweenness centrality play an important role in maintaining the network controllability. Furthermore, taking the reasonable measures for different load failure model can prevent the networks from inducing a step uncontrollable phenomenon.