Failure and recovery in dynamical networks

Böttcher, Lucas; Luković, Mirko; Nagler, Jan; Havlin, Shlomo; Herrmann, Hans J.

doi:10.1038/srep41729

Cited by 56 publications

(66 citation statements)

References 59 publications

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“…Our findings provide an important example of the role played by dynamical correlations in cooperative processes on networked substrates, which is commonly not considered in other theoretical approaches. Pair-approximations as the one developed in this work can be used to improve the accuracy of phase diagrams observed in other related works [52,55] where first order mean-field theory captures the qualitative behavior but analytical spinoidals deviate from simulations when the average connectivity is reduced. Finally, we expect that our work will stimulate future analysis of dynamical correlations on other cooperative processes.…”

Section: Discussionmentioning

confidence: 87%

Dynamical correlations and pairwise theory for the symbiotic contact process on networks

2019

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The two-species symbiotic contact process (2SCP) is a stochastic process where each vertex of a graph may be vacant or host at most one individual of each species. Vertices with both species have a reduced death rate, representing a symbiotic interaction, while the dynamics evolves according to the standard (single species) contact process rules otherwise. We investigate the role of dynamical correlations on the 2SCP on homogeneous and heterogeneous networks using pairwise mean-field theory. This approach is compared with the ordinary one-site theory and stochastic simulations. We show that our approach significantly outperforms the one-site theory. In particular, the stationary state of the 2SCP model on random regular networks is very accurately reproduced by the pairwise mean-field, even for relatively small values of vertex degree, where expressive deviations of the standard mean-field are observed. The pairwise approach is also able to capture the transition points accurately for heterogeneous networks and provides rich phase diagrams with transitions not predicted by the one-site method. Our theoretical results are corroborated by extensive numerical simulations.

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Section: Discussionmentioning

confidence: 87%

Dynamical correlations and pairwise theory for the symbiotic contact process on networks

2019

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“…This should allow to check against a simple oversight in the measurement of the global response ρ via eq. (11) and its interpretation through dynamical scaling.…”

Section: Response Functionmentioning

confidence: 99%

Dynamical universality of the contact process

Böttcher¹,

Herrmann²,

Henkel³

2018

J. Phys. A: Math. Theor.

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The dynamical relaxation and scaling properties of three different variants of the contact process in two spatial dimensions are analysed. Dynamical contact processes capture a variety of contagious processes such as the spreading of diseases or opinions. The universality of both local and global two-time correlators of the particle-density and the associated linear responses are tested through several scaling relations of the non-equilibrium exponents and the shape of the associated scaling functions. In addition, the dynamical scaling of two-time global correlators can be used as a tool to improve on the determination of the location of critical points. * lucasb@ethz.ch arXiv:1802.00037v2 [cond-mat.stat-mech]

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“…Examples include the Internet and World Wide Web, food webs, social networks, transportation systems, electricity distribution networks, genetic networks, brain networks and many others [1][2][3][4][5][6][7][8][9][10][11]. An important concern in the study of complex networks is their robustness, which is important for many fields, such as ecology, biology, economics and engineering [12][13][14][15][16][17][18]. Network robustness deals usually with the question of the response of the network to random failures and targeted attacks.…”

Section: Introductionmentioning

confidence: 99%

Localized attack on networks with clustering

et al. 2019

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Network systems with clustering have been given much attention due to their wide occurrence in the real world. One focus of these studies has been on robustness of single clustered networks and interdependent clustered networks under random attack (RA) or hub-targeted attack. However, infrastructure networks could suffer from a damage that is localized, i.e. a group of neighboring nodes attacked or fail, a topic that was not studied earlier on clustered networks. In this paper, we analytically and via simulations study the robustness under localized attack (LA) of single Erdős-Rényi clustered network and interdependent clustered network. For generating networks with clustering we use two models: (i) double Poisson distribution (DPD) and (ii) fixed degree distribution (FDD). For the LA case, the DPD model shows a second order phase transition behavior for a single clustered network, while for dependent networks, the system undergoes a change of percolation phase transition from a first order (abrupt transition) to a second order (continuous) transition when the coupling strength q decreases below a critical value q c . Our results imply that single networks become significantly more vulnerable with increasing clustering coefficient c with respect to LA. This is in contrast to RA where the robustness is almost independent of c. We obtain similar results when testing different real networks. For LA on dependent networks, we also observe that the system becomes more vulnerable as c increases. This is again in contrast to RA, where for, q<q c , the system robustness is almost unaffected by increasing clustering. We also solved analytically the case of LA on random regular networks which are clustered and interdependent and find that as m (the number of clustered networks that each network depends on) or c increases, the system becomes significantly more vulnerable. We also analyzed via simulations the case of generating clustering in networks for the model of keeping a FDD, and find that the influence of clustering on the robustness of two partially interdependent networks under LA is smaller than for DPD, which is very different from these cases under RA.

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Failure and recovery in dynamical networks

Cited by 56 publications

References 59 publications

Dynamical correlations and pairwise theory for the symbiotic contact process on networks

Dynamical correlations and pairwise theory for the symbiotic contact process on networks

Dynamical universality of the contact process

Localized attack on networks with clustering

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