Abstract
We present a model for the dynamic spreading of failures in networked systems. The model combines network nodes as active, bistable elements and delayed interactions along directed links. By means of simulations, we explore the time-dependent spreading and cascade failures in different network topologies. The results of these simulations point towards a phase transition in the spreading dynamics that depends on node parameters and network topology. In particular, we observe a critical threshold for node recovery. Below this threshold, any disturbance propagates only through a small fraction of the network. The size of this perturbed fraction is determined numerically. Furthermore, we discuss the robustness of networks challenged by coinciding internal failures. Our model may be used to improve disaster preparedness and anticipative disaster response management.
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