Scaling behavior of the contact process in networks with long-range connections

Juhász, Róbert; Ódor, Géza

doi:10.1103/physreve.80.041123

Cited by 14 publications

(10 citation statements)

References 42 publications

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“…In recent years, contact processes on various types of complex networks has attracted significant attention (see, e.g., Refs. [52][53][54][55][56][57][58]). It is interesting to ask whether temporal disorder is a relevant perturbation of the critical behavior of these processes.…”

Section: Discussionmentioning

confidence: 99%

Contact process with temporal disorder

2016

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We investigate the influence of time-varying environmental noise, i.e., temporal disorder, on the nonequilibrium phase transition of the contact process. Combining a real-time renormalization group, scaling theory, and large scale Monte-Carlo simulations in one and two dimensions, we show that the temporal disorder gives rise to an exotic critical point. At criticality, the effective noise amplitude diverges with increasing time scale, and the probability distribution of the density becomes infinitely broad, even on a logarithmic scale. Moreover, the average density and survival probability decay only logarithmically with time. This infinite-noise critical behavior can be understood as the temporal counterpart of infinite-randomness critical behavior in spatially disordered systems, but with exchanged roles of space and time. We also analyze the generality of our results, and we discuss potential experiments.

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Section: Discussionmentioning

confidence: 99%

Contact process with temporal disorder

2016

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“…We have studied generalized small-world (GSW) networks [25][26][27][28][29][30][31][32][33], which consist of a one-dimensional lattice and an additional set of long-range edges of arbitrary, unbounded length. The probability that a pair of sites separated by a distance l is connected by an edge decays with l as…”

Section: -5mentioning

confidence: 99%

Rare-region effects in the contact process on networks

et al. 2012

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Networks and dynamical processes occurring on them have become a paradigmatic representation of complex systems. Studying the role of quenched disorder, both intrinsic to nodes and topological, is a key challenge. With this in mind, here we analyze the contact process (i.e., the simplest model for propagation phenomena) with node-dependent infection rates (i.e., intrinsic quenched disorder) on complex networks. We find Griffiths phases and other rare-region effects, leading rather generically to anomalously slow (algebraic, logarithmic, etc.) relaxation, on Erdős-Rényi networks. We predict similar effects to exist for other topologies as long as a nonvanishing percolation threshold exists. More strikingly, we find that Griffiths phases can also emerge--even with constant epidemic rates--as a consequence of mere topological heterogeneity. In particular, we find Griffiths phases in finite-dimensional networks as, for instance, a family of generalized small-world networks. These results have a broad spectrum of implications for propagation phenomena and other dynamical processes on networks, and are relevant for the analysis of both models and empirical data.

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“…It has been conjectured [17][18][19] that such slow dynamics can occur only in finite dimensional networks as the consequence of heterogeneity: explicit reaction or purely topological disorder. This is based on optimal fluctuation theory and simulations of the contact process (CP) [21,22] on Erdős-Rényi (ER) [20] and on generalized small world networks [23][24][25]. In the case of networks with an infinite topological dimension, like the Barabási-Albert (BA) [26] graph, slow dynamics has been found only in tree networks and weighting schemes, that suppress the information propagation among hubs [27,28].…”

Section: Introductionmentioning

confidence: 99%

Spectral analysis and slow spreading dynamics on complex networks

Ódor

2013

Phys. Rev. E

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The susceptible-infected-susceptible (SIS) model is one of the simplest memoryless systems for describing information or epidemic spreading phenomena with competing creation and spontaneous annihilation reactions. The effect of quenched disorder on the dynamical behavior has recently been compared to quenched meanfield (QMF) approximations in scale-free networks. QMF can take into account topological heterogeneity and clustering effects of the activity in the steady state by spectral decomposition analysis of the adjacency matrix. Therefore, it can provide predictions on possible rare-region effects, thus on the occurrence of slow dynamics. I compare QMF results of SIS with simulations on various large dimensional graphs. In particular, I show that for Erdős-Rényi graphs this method predicts correctly the occurrence of rare-region effects. It also provides a good estimate for the epidemic threshold in case of percolating graphs. Griffiths Phases emerge if the graph is fragmented or if we apply a strong, exponentially suppressing weighting scheme on the edges. The latter model describes the connection time distributions in the face-to-face experiments. In case of a generalized Barabási-Albert type of network with aging connections, strong rare-region effects and numerical evidence for Griffiths Phase dynamics are shown. The dynamical simulation results agree well with the predictions of the spectral analysis applied for the weighted adjacency matrices.

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Scaling behavior of the contact process in networks with long-range connections

Cited by 14 publications

References 42 publications

Contact process with temporal disorder

Contact process with temporal disorder

Rare-region effects in the contact process on networks

Spectral analysis and slow spreading dynamics on complex networks

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