Interdependent resistor networks with process-based dependency

Danziger, Michael M.; Bashan, Amir; Havlin, Shlomo

doi:10.1088/1367-2630/17/4/043046

Cited by 19 publications

(12 citation statements)

References 37 publications

(55 reference statements)

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“…However interdependent percolation is limited to systems where functionality is determined exclusively by connectivity: either to the largest connected component [7], backbone [12] or a set of source nodes [13]. It thus provides only a partial understanding of real-world systems, where the network serves as the base upon which a dynamic process occurs [14,15].…”

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confidence: 99%

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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confidence: 99%

Dynamic interdependence and competition in multilayer networks

et al. 2018

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“…However, this random-like behavior is constrained to the neighborhood of radius z a . Once the damage spreads beyond this neighborhood, it expands linearly in space, with a constant rate and a parabolic decrease in ¥ P , as documented for spatially embedded interdependent networks [31,32,35]. A similar coexistence of random and spatial properties, differentiated by scale, has been observed in the single-layer case [48,63].…”

Section: Resultsmentioning

confidence: 53%

“…Interdependent networks contain layers of networks with two types of links-connectivity links between the nodes in the same layer and dependency links between nodes in different layers. Studies on spatially embedded interdependent networks found that in many cases they are significantly more vulnerable than non-embedded systems [25,[29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

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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“…A study on interdependent resistor networks examined the fraction of nodes that carry current, as well as the overall conductivity of the system in the context of process based dependency [99].…”

Section: Realistic Dependency Relationsmentioning

confidence: 99%

Recent advances on failure and recovery in networks of networks

Shekhtman

Danziger

Havlin

2016

Chaos, Solitons & Fractals

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Until recently, network science has focused on the properties of single isolated networks that do not interact or depend on other networks. However it has now been recognized that many realnetworks, such as power grids, transportation systems, and communication infrastructures interact and depend on other networks. Here we will present a review of the framework developed in recent years for studying the vulnerability and recovery of networks composed of interdependent networks. In interdependent networks, when nodes in one network fail, they cause dependent

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Interdependent resistor networks with process-based dependency

Cited by 19 publications

References 37 publications

Dynamic interdependence and competition in multilayer networks

Dynamic interdependence and competition in multilayer networks

Spreading of localized attacks in spatial multiplex networks

Recent advances on failure and recovery in networks of networks

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