Global robustness versus local vulnerabilities in complex synchronous networks

Tyloo, Melvyn; Jacquod, Philippe

doi:10.1103/physreve.100.032303

Cited by 18 publications

(8 citation statements)

References 49 publications

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“…Examining one random realization of the power grid (Fig. 4 a), we find that, like in the exemplary plant–pollinator network, the MiFaS is associated with a tree-like structure including the most peripheral nodes of the network (according to the resistance centrality proposed by 61 , see Supplementary Fig. S7 ).…”

Section: Resultsmentioning

confidence: 88%

Minimal fatal shocks in multistable complex networks

Halekotte

Feudel

2020

Sci Rep

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Multistability is a common phenomenon which naturally occurs in complex networks. often one of the coexisting stable states can be identified as being the desired one for a particular application. We present here a global approach to identify the minimal perturbation which will instantaneously kick the system out of the basin of attraction of its desired state and hence induce a critical or fatal transition we call shock-tipping. the corresponding Minimal Fatal Shock is a vector whose length can be used as a global stability measure and whose direction in state space allows us to draw conclusions on weaknesses of the network corresponding to critical network motifs. We demonstrate this approach in plant-pollinator networks and the power grid of Great Britain. in both system classes, tree-like substructures appear to be the most vulnerable with respect to the minimal shock perturbation. Many processes in nature can be well described in terms of nonlinear dynamical systems possessing multiple stable states for constant external conditions 1,2. As long as perturbations are small, it is sufficient to consider the linearized problem around an attracting state to evaluate its 'local' stability. However, in real systems, the most threatening perturbations are usually not small but large, even constituting extreme events like storms, earthquakes or financial crises 3-5. Obviously, large perturbations in multistable systems call for a 'global' stability paradigm. Adequate frameworks have been introduced in the ecological literature-by Holling 6,7-as well as in the engineering literature-by Soliman and Thompson 8 (see 9 for a recent review)-who both argued that the local approach to stability needs to be accompanied by non-local measures capturing the characteristics of a state's basin of attraction. Recently, this global approach has been picked up in the field of complex networks in which multistability and large disturbances occur naturally as well 10-14. Suitable aspects of a basin of attraction are its size, shape and depth, which until now have all been used-separately 15-19 or in combination 20-22-to measure the stability of multistable systems. The suitability of a certain stability criterion for a specific problem also depends on the shape or distribution of the perturbations that occur. If perturbations are best described as noise, a suitable approach is to analyze the most likely escape path from the basin of attraction 23-25. This path is determined by the position of the saddle point on the basin boundary possessing the lowest barrier to escape 26. A very different situation occurs if perturbations are singular, large and abrupt. The response of nonlinear systems to such perturbations has been considered in terms of linear response theory as well as transient dynamics in climate science 27 , fluid dynamics 28,29 and energy networks 18,30,31. In networks, the most frequently applied characteristic to measure a system's stability against large abrupt perturbations is the relative basin size which is usually esti...

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Section: Resultsmentioning

confidence: 88%

Minimal fatal shocks in multistable complex networks

Halekotte

Feudel

2020

Sci Rep

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“…To determine the vulnerability measure of this node we set ωk (t) to a time dependent, Ornstein-Uhlenbeck noise disturbance, and ωs = 0 for all s = k. Let θ(k) i be a corresponding solution of (2). 2 We then define…”

Section: A Vulnerability Measurementioning

confidence: 99%

“…C OMPLEX networks are frequently used to model coupled dynamical systems ranging from interacting molecules in chemical reactions [1] to high voltage electric grids [2]. Be it man-made or natural, elements of a coupled dynamical system are represented by nodes in a complex network, and two nodes are adjacent to one another if the differential equations that govern those nodes, are dependent on one another [2]. Two questions that are often investigated in complex networks are:…”

Section: Introductionmentioning

confidence: 99%

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Designing for Robustness in Electric Grids via a General Effective Resistance Measure

Nagpal¹,

Nair²,

Parise³

et al. 2022

Preprint

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We propose a mathematical framework for designing robust networks of coupled phase-oscillators by leveraging a vulnerability measure proposed by Tyloo et. al that quantifies how much a small perturbation to a phaseoscillator's natural frequency impacts the system's global synchronized frequencies. Given a fixed complex network topology with specific governing dynamics, the proposed framework finds an optimal allocation of edge weights that minimizes such vulnerability measure(s) at the node(s) for which we expect perturbations to occur by solving a tractable semidefinite programming problem. We specify the mathematical model to high voltage electric grids where each node corresponds to a voltage phase angle associated with a bus and edges correspond to transmission lines. Edge weights are determined by the susceptance values along the transmission lines. In this application, frequency synchronization is increasingly challenged by the integration of renewable energy, yet is imperative to the grid's health and functionality. Our framework helps to alleviate this challenge by optimizing the placement of renewable generation and the susceptance values along the transmission lines.

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“…Relevant literatures are available in [16]- [18]. In recent years, many scholars have studied resistive distance in different aspects of complex network, such as community detection [19]- [23], centrality measures [24]- [26], link prediction problem [27] and network robustness [28]- [31], etc. By the way, resistance in the network is intimately connected with the lengths of random walks on the graph.…”

Section: Introductionmentioning

confidence: 99%

Novel Resistive Distance Descriptors on Complex Network

Zhou

Lin

et al. 2022

IEEE Access

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Large-scale complex network data poses significant challenges for the analytic ideas and tools to monitor and analyze complex networks. As classical structure descriptors, average path length (L), global and local network efficiency (E glob and E loc ), general and loop clustering coefficient (C 3 and D), play significant roles in complex network analysis. In this paper, we make use of resistive distance instead of the shortest path distance to suggest resistive distance descriptors, i.e., L r , Ω glob and Ω loc , Ω 3 and D r . We investigate all the resistive descriptors on classical WS, BA and ER models and find some interesting phenomenons. On one hand, L r and Ω 3 (resp., Ω glob and Ω loc ) can be used to characterize the features of small-word networks. On the other hand, L r , Ω 3 , and Ω glob can be utilized to measure network invulnerability. To access the effectiveness of the resistive distance descriptors, we conduct extensive numerical simulations on synthetic and real networks. In comparison with the baselines, the proposed metrics show competitive performance on classical network models and are more efficient for networks with small and medium size.

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Global robustness versus local vulnerabilities in complex synchronous networks

Cited by 18 publications

References 49 publications

Minimal fatal shocks in multistable complex networks

Minimal fatal shocks in multistable complex networks

Designing for Robustness in Electric Grids via a General Effective Resistance Measure

Novel Resistive Distance Descriptors on Complex Network

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