Langevin approach for the dynamics of the contact process on annealed scale-free networks

Marián Boguñá, Claudio Castellano, and Romualdo Pastor-Satorras
Phys. Rev. E 79, 036110 – Published 19 March 2009

Abstract

We study the dynamics of the contact process, one of the simplest nonequilibrium stochastic processes, taking place on a scale-free network. We consider the network topology as annealed, i.e., all links are rewired at each microscopic time step, so that no dynamical correlation can build up. This is a practical implementation of the absence of correlations assumed by mean-field approaches. We present a detailed analysis of the contact process in terms of a Langevin equation, including explicitly the effects of stochastic fluctuations in the number of particles in finite networks. This allows us to determine analytically the survival time for spreading experiments and the density of active sites in surviving runs. The fluctuations in the topological structure induce anomalous scaling effects with respect to the system size when the degree distribution has a hard upper bound. When the upper bound is soft, the presence of outliers with huge connectivity perturbs the picture even more, inducing an apparent shift of the critical point. In light of these findings, recent theoretical and numerical results in the literature are critically reviewed.

    • Received 16 October 2008

    DOI:https://doi.org/10.1103/PhysRevE.79.036110

    ©2009 American Physical Society

    Authors & Affiliations

    Marián Boguñá1, Claudio Castellano2, and Romualdo Pastor-Satorras3

    • 1Departament de Física Fonamental, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
    • 2SMC, INFM-CNR, and Dipartimento di Fisica, “Sapienza” Università di Roma, Piazzale Aldo Moro 2, I-00185 Roma, Italy
    • 3Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain

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    Issue

    Vol. 79, Iss. 3 — March 2009

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