Quasistationary analysis of the contact process on annealed scale-free networks

Ferreira, Silvio C.; Ferreira, Ronan Silva; Pastor-Satorras, Romualdo

doi:10.1103/physreve.83.066113

Cited by 52 publications

(111 citation statements)

References 32 publications

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“…Such a dependence (which both previous FSS approaches were lacking) introduces very strong corrections to scaling. However, if such corrections are properly taken into account, it is possible to show that the CP on annealed networks agrees, with high accuracy, with the predictions of HMF theory [16].…”

Section: Introductionmentioning

confidence: 79%

Quasistationary simulations of the contact process on quenched networks

et al. 2011

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We present high-accuracy quasistationary (QS) simulations of the contact process in quenched networks, built using the configuration model with both structural and natural cutoffs. The critical behavior is analyzed in the framework of the anomalous finite-size scaling which was recently shown to hold for the contact process on annealed networks. It turns out that the quenched topology does not qualitatively change the critical behavior, leading only (as expected) to a shift of the transition point. The anomalous finite-size scaling holds with exactly the same exponents of the annealed case, so we can conclude that heterogeneous mean-field theory works for the contact process on quenched networks, at odds with previous claims. Interestingly, topological correlations induced by the presence of the natural cutoff do not alter the picture.

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Section: Introductionmentioning

confidence: 79%

Quasistationary simulations of the contact process on quenched networks

et al. 2011

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“…To see corrections to scaling, I have plotted the effective decay exponents Eq. (13) in the left inset of Fig. 4.…”

Section: Sis Model Simulations On Weighted Treesmentioning

confidence: 99%

“…In particular, in the case of ubiquitous scale-free (SF) networks [10], exhibiting P (k) ∼ k −γ degree distribution of the nodes [6,7] the location of the phase transition and the singular behavior is still a debated issue. Numerical simulations [11][12][13][14] and theoretical approaches based on the heterogeneous mean-field (HMF) theory [11,12,15] show strong effects of the network heterogeneity on the behavior of the CP defined on complex networks.…”

Section: Introductionmentioning

confidence: 99%

Rare regions of the susceptible-infected-susceptible model on Barabási-Albert networks

Ódor

2013

Phys. Rev. E

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I extend a previous work to susceptible-infected-susceptible (SIS) models on weighted Barabási-Albert scale-free networks. Numerical evidence is provided that phases with slow, power-law dynamics emerge as the consequence of quenched disorder and tree topologies studied previously with the contact process. I compare simulation results with spectral analysis of the networks and show that the quenched mean-field (QMF) approximation provides a reliable, relatively fast method to explore activity clustering. This suggests that QMF can be used for describing rare-region effects due to network inhomogeneities. Finite-size study of the QMF shows the expected disappearance of the epidemic threshold λ c in the thermodynamic limit and an inverse participation ratio ∼0.25, meaning localization in case of disassortative weight scheme. Contrarily, for the multiplicative weights and the unweighted trees, this value vanishes in the thermodynamic limit, suggesting only weak rare-region effects in agreement with the dynamical simulations. Strong corrections to the mean-field behavior in case of disassortative weights explains the concave shape of the order parameter ρ(λ) at the transition point. Application of this method to other models may reveal interesting rare-region effects, Griffiths phases as the consequence of quenched topological heterogeneities.

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“…In particular, it has been shown that its absorbing phase transition exhibits a nontrivial finite-size scaling [16], depending not only on the number of vertices N , but also on the degree fluctuations of the network, measured by the second moment of the degree distribution k 2 = k k 2 P (k). This dependence induces very strong corrections to scaling in SF networks, which, if properly taken into account, can actually be observed in numerical simulations [13,14].…”

Section: Introductionmentioning

confidence: 99%

“…Thus, for λ < λ c , an absorbing phase with ρ = 0 is observed, while for λ > λ c the system reaches an active phase, with ρ > 0 in the thermodynamic limit. Through a systematic analysis relying on numerical simulations [11][12][13][14] and theoretical approaches based on the heterogeneous meanfield (HMF) theory [11,12,15] a picture has emerged of the behavior of the CP on complex networks that emphasizes the strong effects of the network heterogeneity. In particular, it has been shown that its absorbing phase transition exhibits a nontrivial finite-size scaling [16], depending not only on the number of vertices N , but also on the degree fluctuations of the network, measured by the second moment of the degree distribution k 2 = k k 2 P (k).…”

Section: Introductionmentioning

confidence: 99%

Slow dynamics and rare-region effects in the contact process on weighted tree networks

Ódor

Pastor-Satorras

2012

Phys. Rev. E

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We show that generic, slow dynamics can occur in the contact process on complex networks with a tree-like structure and a superimposed weight pattern, in the absence of additional (nontopological) sources of quenched disorder. The slow dynamics is induced by rare-region effects occurring on correlated subspaces of vertices connected by large weight edges and manifests in the form of a smeared phase transition. We conjecture that more sophisticated network motifs could be able to induce Griffiths phases, as a consequence of purely topological disorder.

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Quasistationary analysis of the contact process on annealed scale-free networks

Cited by 52 publications

References 32 publications

Quasistationary simulations of the contact process on quenched networks

Quasistationary simulations of the contact process on quenched networks

Rare regions of the susceptible-infected-susceptible model on Barabási-Albert networks

Slow dynamics and rare-region effects in the contact process on weighted tree networks

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