Recent advances on failure and recovery in networks of networks

Shekhtman, Louis; Danziger, Michael M.; Havlin, Shlomo

doi:10.1016/j.chaos.2016.02.002

Cited by 96 publications

(46 citation statements)

References 103 publications

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“…1 for more details). Solutions of the system (17), shows that the population of oscillators in each layer splits into two groups, namely drifting and frequency locked oscillators [66]. The phases of the latter ones are entrained by the mean-field and correspond to fixed point solutions of the system (15), i.e.φ σ = 0.…”

Section: Methodsmentioning

confidence: 99%

“…Here, we propose a general framework for modelling interactions between dynamical systems. Two fundamental and ubiquitous ways in which nodes in one system can influence nodes in another one are interdependency or cooperation, as in critical infrastructures [11,16,17] or among financial networks [18,19], and competition or antagonism, which is common in ecological systems [20,21], social networks [4], or in the human brain [1,22]. It is not uncommon to find interdependent and competitive interactions simultaneously, in predator-prey relationships in ecological systems [23], in binocular rivalry in the brain [24], or even in phenomena like "frenemies" and "coopetition" in social systems [25].…”

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confidence: 99%

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Dynamic interdependence and competition in multilayer networks

et al. 2018

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From critical infrastructure, to physiology and the human brain, complex systems rarely occur in isolation. Instead, the functioning of nodes in one system often promotes or suppresses the functioning of nodes in another. Despite advances in structural interdependence, modeling interdependence and other interactions between dynamic systems has proven elusive. Here we define a broadly applicable dynamic dependency link and develop a general framework for interdependent and competitive interactions between general dynamic systems. We apply our framework to studying interdependent and competitive synchronization in multi-layer oscillator networks and cooperative/competitive contagions in an epidemic model. Using a mean-field theory which we verify numerically, we find explosive transitions and rich behavior which is absent in percolation models including hysteresis, multi-stability and chaos. The framework presented here provides a powerful new way to model and understand many of the interacting complex systems which surround us. * Electronic address: michael.danziger@biu.ac.il † Electronic address: ivan.bms.2011@gmail.com but without a general framework or ability to uncover universal patterns between systems [26-28].arXiv:1705.00241v1 [cond-mat.stat-mech]

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Section: Methodsmentioning

confidence: 99%

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confidence: 99%

Dynamic interdependence and competition in multilayer networks

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“…Buldyrev et al developed a model of interdependent networks and found analytically that the percolation transition is discontinuous due to the emergence of cascading failures between the networks. A framework for understanding the robustness of interdependent networks was then developed, and found that a system of interdependent networks undergoes an abrupt first-order percolation phase transition [27][28][29][30][31][32][33][34].…”

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confidence: 99%

Resilience of networks with community structure behaves as if under an external field

Dong

Fan

Shekhtman

et al. 2018

Proc. Natl. Acad. Sci. U.S.A.

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Although detecting and characterizing community structure is key in the study of networked systems, we still do not understand how community structure affects systemic resilience and stability. We use percolation theory to develop a framework for studying the resilience of networks with a community structure. We find both analytically and numerically that interlinks (the connections among communities) affect the percolation phase transition in a way similar to an external field in a ferromagnetic- paramagnetic spin system. We also study universality class by defining the analogous critical exponents and, and we find that their values in various models and in real-world coauthor networks follow the fundamental scaling relations found in physical phase transitions. The methodology and results presented here facilitate the study of network resilience and also provide a way to understand phase transitions under external fields.

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“…In figure 5, we see that the cascade begins random-like, with no spatial influence within the neighborhood of the failure and a random branching process with expected branching factor of »1, as established for interdependent random networks [28,60,62]. However, this random-like behavior is constrained to the neighborhood of radius z a .…”

Section: Resultsmentioning

confidence: 64%

Spreading of localized attacks in spatial multiplex networks

2017

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Many real-world multilayer systems such as critical infrastructure are interdependent and embedded in space with links of a characteristic length. They are also vulnerable to localized attacks or failures, such as terrorist attacks or natural catastrophes, which affect all nodes within a given radius. Here we study the effects of localized attacks on spatial multiplex networks of two layers. We find a metastable region where a localized attack larger than a critical size induces a nucleation transition as a cascade of failures spreads throughout the system, leading to its collapse. We develop a theory to predict the critical attack size and find that it exhibits novel scaling behavior. We further find that localized attacks in these multiplex systems can induce a previously unobserved combination of random and spatial cascades. Our results demonstrate important vulnerabilities in real-world interdependent networks and show new theoretical features of spatial networks.

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Recent advances on failure and recovery in networks of networks

Cited by 96 publications

References 103 publications

Dynamic interdependence and competition in multilayer networks

Dynamic interdependence and competition in multilayer networks

Resilience of networks with community structure behaves as if under an external field

Spreading of localized attacks in spatial multiplex networks

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