Rare-region effects in the contact process on networks

Róbert Juhász, G. Ódor, Claudio Castellano, Miguel A. Muñoz

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

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 Erdos-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.

Original languageEnglish
Article number066125
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume85
Issue number6
DOIs
Publication statusPublished - Jun 20 2012

Fingerprint

Contact Process
Quenched Disorder
Propagation
Small-world Network
Percolation Threshold
Vertex of a graph
Erdös
disorders
Complex Networks
Infection
Complex Systems
Logarithmic
propagation
infectious diseases
Topology
complex systems
Predict
Dependent
topology
Model

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Rare-region effects in the contact process on networks. / Juhász, Róbert; Ódor, G.; Castellano, Claudio; Muñoz, Miguel A.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 85, No. 6, 066125, 20.06.2012.

Research output: Contribution to journalArticle

Juhász, Róbert ; Ódor, G. ; Castellano, Claudio ; Muñoz, Miguel A. / Rare-region effects in the contact process on networks. In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2012 ; Vol. 85, No. 6.
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