Out of control: Fluctuation of cascading dynamics in networks

Applying two preferential selection mechanisms of flow destination, we develop two new methods to quantify the initial load of a node, where the flow is transported along the shortest path between two nodes. We propose a simple cascading model and study cascading dynamics induced by attacking the node with the highest load in some synthetic and actual networks. Surprisingly, we observe the abnormal fluctuation of cascading dynamics, i.e., more damage can be triggered if we spend significantly higher cost to protect a network. In particular, this phenomenon is independent of the initial flow distribution and the preferential selection mechanisms of flow destination. However, it remains unclear which specific structural patterns may affect the fluctuation of cascading dynamics. In this paper, we examine the local evolution of the cascading propagation by constructing some special networks. We show that revivals of some nodes in the double ring structure facilitate the transportation of the flow between two unconnected sub-networks, cause more damage and subsequently lead to the abnormal fluctuation of cascading dynamics. Compared with the traditional definition of the betweenness, we adopt two new proposed methods to further evaluate the resilience of several actual networks. We find that some real world networks reach the strongest resilience level against cascading failures in our preferential selection mechanisms of flow destination. Moreover, we explore how to use the minimum cost to maximize the resilience of the studied networks.