Stress induced degradation dynamics in complex networks

Wide-area breakdowns of infrastructure networks often result from an initial, relatively slow system degradation that eventually evolves into a fast and uncontrollable failure propagation sequence, as has been observed on cascading line outages within electric power grids. In order to study the global dynamics of such failure processes in complex networks we introduce a generic model which considers two stress induced component outage types differing from each other in their time-scale. In the first case the failure is due to an increase in the nodal stress above a critical level and occurs after a small time delay. In analogy to an accelerated ageing process, the second failure type takes the whole history of stress into account. The two failure modes are coupled by simple differential equations. The focus of this paper is set on the influence of different topologies on the progression of the two failure types in time and on the resulting node outage sequence leading to network collapse. Furthermore, the importance of the different model parameters are discussed.