Oscillations in complex communication networks under attack

In this paper we study the traffic dynamics of a scale-free complex network under an intentional attack at the node with the largest betweenness (i.e., the hub). This node is removed from the network after the attack. Consequently, the traffic load which used to go through the hub has to find other paths. A weight is defined for each node to indicate how long a packet has to wait at this node. A shortest time delay routing strategy is then applied based on the weight. We find that with different values of the capacity redundancy parameter, the traffic dynamics are quite different. When the capacity has large redundancy, then all the nodes work in a free-flow state even after the attack. If the capacity redundancy is not that large, then congestion may occur at some nodes. Due to the shortest time delay routing strategy, this congestion occurs periodically. If the capacity is very small, then the traffic dynamics become complicated, and oscillations and chaotic phenomena take place.