Catastrophic and major disasters in real-world systems, such as blackouts in power grids or global failures in critical infrastructures, are often triggered by minor events which originate a cascading failure in interdependent graphs. We present here a self-consistent theory enabling the systematic analysis of cascading failures in such networks and encompassing a broad range of dynamical systems, from epidemic spreading, to birth–death processes, to biochemical and regulatory dynamics. We offer testable predictions on breakdown scenarios, and, in particular, we unveil the conditions under which the percolation transition is of the first-order or the second-order type, as well as prove that accounting for dynamics in the nodes always accelerates the cascading process. Besides applying directly to relevant real-world situations, our results give practical hints on how to engineer more robust networked systems.
We explore the robustness of a network against failures of vertices or edges where a fraction f of vertices is removed and an overload model based on betweenness is constructed. It is assumed that the load and capacity of vertex i are correlated with its betweenness centrality Bi
as
B
i
θ
and
(
1
+
α
)
B
i
θ
(θ is the strength parameter, α is the tolerance parameter). We model the cascading failures following a local load preferential sharing rule. It is found that there exists a minimal α
c when θ is between 0 and 1, and its theoretical analysis is given. The minimal α
c characterizes the strongest robustness of a network against cascading failures triggered by removing a random fraction f of vertices. It is realized that the minimal α
c increases with the increase of the removal fraction f or the decrease of average degree. In addition, we compare the robustness of networks whose overload models are characterized by degree and betweenness, and find that the networks based on betweenness have stronger robustness against the random removal of a fraction f of vertices.
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