Spreading of localized attacks in spatial multiplex networks

Vaknin, David; Danziger, Michael M.; Havlin, Shlomo

doi:10.1088/1367-2630/aa7b09

Cited by 56 publications

(55 citation statements)

References 72 publications

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“…The homogeneous model studied in [13,15,17,18] assumes two dimensional grid size L × L with L being the lattice length. The construction of the model consists of the following stages: (i) a single node is randomly chosen.…”

Section: Heterogeneous and Homogeneous Spatial Modelsmentioning

confidence: 99%

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Two transitions in spatial modular networks

et al. 2020

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Understanding the resilience of infrastructures, such as a transportation network, has significant importance for our daily life. Recently, a homogeneous spatial network model was developed for studying spatial embedded networks with characteristic link length such as power-grids and the brain. However, although many real-world networks are spatially embedded and their links have characteristics length such as pipelines, power lines or ground transportation lines they are not homogeneous but rather heterogeneous. For example, density of links within cities are significantly higher than between cities. Here we develop and study numerically and analytically a similar realistic heterogeneous spatial modular model using percolation process to better understand the effect of heterogeneity on such networks. The model assumes that inside a city there are many lines connecting different locations, while long lines between the cities are sparse and usually directly connecting only a few nearest neighbours cities in a two dimensional plane. We find that our heterogeneous model experiences two distinct continuous transitions, one when the cities disconnect from each other and the second when each city breaks apart. This is in contrast to the homogeneous model where a single transition is found. Although the critical threshold for site percolation in 2D grid remains an open question we analytically find the critical threshold for site percolation in this model. In addition, it has been found that the homogeneous model experience a single transition having a unique phenomenon called critical stretching where a geometric crossover from random to spatial structure in different scales found to stretch non-linearly with the characteristic length at criticality. In marked contrast, we show here that the heterogeneous model does not experience such a phenomenon indicating that critical stretching strongly depends on the network structure.

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Section: Heterogeneous and Homogeneous Spatial Modelsmentioning

confidence: 99%

“…One of the most important properties of a network is its structure. The structure of a network can vary in many ways such as interplay between random to spatial structure [13][14][15][16][17][18], different degree distribution [19], clustering [20,21] or community structure [22][23][24][25] which have a significant effect on the phenomena that appear on it.…”

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confidence: 99%

Two transitions in spatial modular networks

et al. 2020

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“…In general, our proposed strategy can maximum to avoid change the network topology through establishing a new link between adjacent neighbors of failed node, and be more applicability. [20,36].…”

Section: Fig6mentioning

confidence: 99%

“…In short, the main difference between localized attacks and random attacks is that the former always limited to a local area, while the latter are global attacks and the failures are distributed throughout the whole system. Recently research reveals that failures in systems are often not random, but geographically localized attacks [20]. Moreover, such localized attacks results in an extreme instability of interdependent spatially embedded networks since a small failures can trigger an avalanche [21].…”

Section: Introductionmentioning

confidence: 99%

The Effective Healing Strategy against Localized Attacks on Interdependent Spatially Embedded Networks

Gong

Liu

et al. 2019

Complexity

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Many real infrastructure networks, such as power grids and communication networks, are not only depend on one another to function, but also embedded in space. A lot of works have been devoted to reveal the vulnerability of interdependent spatially embedded networks considers random failures. However, recently research show that they are susceptible to geographically localized attacks or failures cased by natural disasters or terrorist attacks, which affect all nodes within a given radius. In particular, small localized attacks may lead to catastrophic consequences. As a remedy of the collapse instability, one research introduced a dynamic healing strategy and the possibility of new connectivity link with a probability, called random healing, to bridge two remaining neighbors of a failed node. The random strategy is straightforward. Here, unlike previous strategy, we propose a simple but effective strategy, called healing strategy by prioritizing minimum degree(HPMD), which establishing a new link between two functioning neighbors with minimum degree during the cascading failures. In addition, we consider the distance between two nodes to avoid change the network structures. Afterwards, a comparison is made between HPMD and three healing strategies: random, degree centrality and local centrality to identify which a pair of neighbors have high priority. Simulation experiments are presented for two square lattices with the same size as interdependent spatially embedded networks under localized attacks. Results demonstrated that HPMD strategy has an outstanding performance against localized attacks, even when ratio of healing is vary. Moreover, HPMD is more timely, more applicability and costless. Our method is meaningful in practice as it can greatly enhance the resilience and robustness of interdependent spatially embedded networks against localized attacks, and eradicate catastrophic collapse in spatial system. keywords: interdependent spatially embedded networks, localized attacks, cascading failures, healing strategy corresponding

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“…However, in most cases, multivariate time series, as a record or mirror of real-world systems, exhibit obvious multiple characteristics. Multilayer network [23][24][25][26][27][28], possessing large number of nodes in multiple layers with different types of edges, allows providing a more intuitive and accurate characterization of multivariate time series. Plenty of successful applications have been achieved in diverse fields involving social network [29], multiphase flow [30], transportation system [31], biological systems [32], and information spreading [33,34].…”

Section: Introductionmentioning

confidence: 99%

A novel time-frequency multilayer network for multivariate time series analysis

Dang

Gao

et al. 2018

New J. Phys.

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Unveiling complex dynamics of natural systems from a multivariate time series represents a research hotspot in a broad variety of areas. We develop a novel multilayer network analysis framework, i.e. multivariate time-frequency multilayer network (MTFM network), to peer into the complex system dynamics. Through mapping the system features into different frequency-based layers and inferring interactions (edges) among different channels (nodes), the MTFM network allows efficiently integrating time, frequency and spatial information hidden in a multivariate time series. We employ two dynamic systems to illustrate the effectiveness of the MTFM network. We first apply the MTFM network to analyze the 48-channel measurements from industrial oil-water flows and reveal the complex dynamics ruling the transition of different flow patterns. The MTFM network is then utilized to analyze 30-channel fatigue driving electroencephalogram signals. The results demonstrate that MTFM network enables to quantitatively characterize brain behavior associated with fatigue driving. Our MTFM network enriches the multivariate time series analysis theory and helps to better understand the complicated dynamical behaviors underlying complex systems.

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Spreading of localized attacks in spatial multiplex networks

Cited by 56 publications

References 72 publications

Two transitions in spatial modular networks

Two transitions in spatial modular networks

The Effective Healing Strategy against Localized Attacks on Interdependent Spatially Embedded Networks

A novel time-frequency multilayer network for multivariate time series analysis

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