Localized attacks on spatially embedded networks with dependencies.
Bottom Line:
We develop a theoretical and numerical approach to describe and predict the effects of localized attacks on spatially embedded systems with dependencies.Though robust to random failures-even of finite fraction-if subjected to a localized attack larger than a critical size which is independent of the system size (i.e., a zero fraction), a cascading failure emerges which leads to complete system collapse.Our results demonstrate the potential high risk of localized attacks on spatially embedded network systems with dependencies and may be useful for designing more resilient systems.
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Affiliation: Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel.
ABSTRACT
Many real world complex systems such as critical infrastructure networks are embedded in space and their components may depend on one another to function. They are also susceptible to geographically localized damage caused by malicious attacks or natural disasters. Here, we study a general model of spatially embedded networks with dependencies under localized attacks. We develop a theoretical and numerical approach to describe and predict the effects of localized attacks on spatially embedded systems with dependencies. Surprisingly, we find that a localized attack can cause substantially more damage than an equivalent random attack. Furthermore, we find that for a broad range of parameters, systems which appear stable are in fact metastable. Though robust to random failures-even of finite fraction-if subjected to a localized attack larger than a critical size which is independent of the system size (i.e., a zero fraction), a cascading failure emerges which leads to complete system collapse. Our results demonstrate the potential high risk of localized attacks on spatially embedded network systems with dependencies and may be useful for designing more resilient systems. No MeSH data available. Related in: MedlinePlus |
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Mentions: We find that is entirely determined by the average degree 〈k〉 and the maximal dependency link length r. These are intensive system quantities and therefore does not grow with system size (Fig. 1d). Figs. 2c and 2d show how the critical damage size changes with respect to 〈k〉 and r for a system of size L × L = 1000 × 1000. In Fig. 2c we can see that the metastable region covers a wider range of 〈k〉 values when r increases. In the metastable phase, for every r, increases with 〈k〉 and jumps up dramatically at a certain 〈k〉 value which represents the end of the metastable phase and the beginning of the stable phase. Furthermore, we see that this jump occurs at larger 〈k〉 values for larger r values (Fig. 2c). In Fig. 2d, we see that above a certain minimum value, has an approximately linear dependence on r in the metastable region. This is due to the fact that a larger r means that a given node's dependency link can be located farther away. Thus the secondary damage from the localized attack is more dispersed and a larger attack size is required to initiate a cascade. Furthermore, we find that the critical damage size takes a minimal value and the system is most susceptible to small local attacks when r is near the stable phase. Extensive numerical simulations of over a high resolution grid of parameters 〈k〉 and r is shown in Fig. 2a and the theoretical prediction which is in good agreement is given in Fig. 2b. The theoretical description of the effect of 〈k〉 and r on is presented below. |
View Article: PubMed Central - PubMed
Affiliation: Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel.
No MeSH data available.