Abstract
The emergence and evolution of real-world systems have been extensively studied in the last few years. However, equally important phenomena are related to the dynamics of systems’ collapse, which has been less explored, especially when they can be cast into interdependent systems. In this paper, we develop a dynamical model that allows scrutinizing the collapse of systems composed of two interdependent networks. Specifically, we explore the dynamics of the system’s collapse under two scenarios: in the first one, the condition for failure should be satisfied for the focal node as well as for its corresponding node in the other network; while in the second one, it is enough that failure of one of the nodes occurs in either of the two networks. We report extensive numerical simulations of the dynamics performed in different setups of interdependent networks, and analyze how the system behavior depends on the previous scenarios as well as on the topology of the interdependent system. Our results can provide valuable insights into the crashing dynamics and evolutionary properties of interdependent complex systems.
Highlights
The emergence and evolution of real-world systems have been extensively studied in the last few years
We have performed extensive numerical simulations of the dynamics described in the previous section on top of interdependent networks generated as described earlier
In the top three panels [(a),(b),(c)], we show results for the “AND” rule, which is applied at each iterative time step, that is, a pair of nodes will be removed from the network with probability f if and only if both of the corresponding partners on two interdependent networks fulfill the leaving condition
Summary
The emergence and evolution of real-world systems have been extensively studied in the last few years. A very recent work[37], has opened the path to bridge this gap, where Yang et al.[37] used data from North-American power grids to show that there exists a vulnerable set of nodes in the system that mainly consists of a small but topologically central portion of the network, with large cascades disproportionately emerging at or triggered by initial failures close to this set. Despite these recent advances, a current challenge is to develop a general approach to model the dynamics of cascading failures. Apart from adding more realism to the model since node heterogeneity is a defining feature of many real-world networks, numerical simulations showed[39] that the crashing behavior can be greatly affected by this kind of heterogeneity
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