Failure-recovery model with competition between failures in complex networks: a dynamical approach

Valdez, Lucas D.; Muro, M. A. Di; Braunstein, Lidia A.

doi:10.1088/1742-5468/2016/09/093402

Cited by 13 publications

(11 citation statements)

References 32 publications

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“…Triple points shown in the phase diagrams depend on connectivity, departing from (λ t , µ t ) = (1, 1/2) for the complete graph (one-site meanfield) [24] to λ t = k k −1 and µ t = 0.501(1), 0.545 (5), and 0.595(5) for k = 10 3 , 20, and 6, respectively. It worths to comment that phase diagrams with qualitatively similar spinoidals found in 2SCP with our PMF theory have been reported for other models with abrupt transitions on networks [52][53][54] with a difference that they were obtained by a first-order mean-field theory, whereas in the 2SCP model we needed to go up to a second-order pairwise theory. Figure 5(a) also presents the phase diagram obtained via simulations on different graphs with average degree k = 6.…”

Section: Resultssupporting

confidence: 75%

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: Resultssupporting

confidence: 75%

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

2019

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“…We investigate this behavior by studying the Lyapunov function 48 as very recently reported in ref. 57 . In our case, the Lyapunov function V ( a, u int ) is derived from the following equations ( α, β > 0):…”

Section: Resultsmentioning

confidence: 99%

Failure and recovery in dynamical networks

Böttcher

Luković

Nagler

et al. 2017

Sci Rep

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Failure, damage spread and recovery crucially underlie many spatially embedded networked systems ranging from transportation structures to the human body. Here we study the interplay between spontaneous damage, induced failure and recovery in both embedded and non-embedded networks. In our model the network’s components follow three realistic processes that capture these features: (i) spontaneous failure of a component independent of the neighborhood (internal failure), (ii) failure induced by failed neighboring nodes (external failure) and (iii) spontaneous recovery of a component. We identify a metastable domain in the global network phase diagram spanned by the model’s control parameters where dramatic hysteresis effects and random switching between two coexisting states are observed. This dynamics depends on the characteristic link length of the embedded system. For the Euclidean lattice in particular, hysteresis and switching only occur in an extremely narrow region of the parameter space compared to random networks. We develop a unifying theory which links the dynamics of our model to contact processes. Our unifying framework may help to better understand controllability in spatially embedded and random networks where spontaneous recovery of components can mitigate spontaneous failure and damage spread in dynamical networks.

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“…Without resource support a node recovers spontaneously at a rate m 0 [35], and for simplicity we assume m = 0 0 . The recovery rate of i at time t is…”

Section: Epidemic Model With Social-supportmentioning

confidence: 99%

Suppressing epidemic spreading in multiplex networks with social-support

et al. 2018

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Although suppressing the spread of a disease is usually achieved by investing in public resources, in the real world only a small percentage of the population have access to government assistance when there is an outbreak, and most must rely on resources from family or friends. We study the dynamics of disease spreading in social-contact multiplex networks when the recovery of infected nodes depends on resources from healthy neighbors in the social layer. We investigate how degree heterogeneity affects the spreading dynamics. Using theoretical analysis and simulations we find that degree heterogeneity promotes disease spreading. The phase transition of the infected density is hybrid and increases smoothly from zero to a finite small value at the first invasion threshold and then suddenly jumps at the second invasion threshold. We also find a hysteresis loop in the transition of the infected density. We further investigate how an overlap in the edges between two layers affects the spreading dynamics. We find that when the amount of overlap is smaller than a critical value the phase transition is hybrid and there is a hysteresis loop, otherwise the phase transition is continuous and the hysteresis loop vanishes. In addition, the edge overlap allows an epidemic outbreak when the transmission rate is below the first invasion threshold, but suppresses any explosive transition when the transmission rate is above the first invasion threshold.

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Failure-recovery model with competition between failures in complex networks: a dynamical approach

Cited by 13 publications

References 32 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

Failure and recovery in dynamical networks

Suppressing epidemic spreading in multiplex networks with social-support

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