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

Marcelo M. de Oliveira, Sidiney G. Alves, and Silvio C. Ferreira
Phys. Rev. E 100, 052302 – Published 4 November 2019

Abstract

The two-species symbiotic contact process (2SCP) is a stochastic process in which 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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  • Received 12 September 2019

DOI:https://doi.org/10.1103/PhysRevE.100.052302

©2019 American Physical Society

Physics Subject Headings (PhySH)

NetworksStatistical Physics & ThermodynamicsInterdisciplinary Physics

Authors & Affiliations

Marcelo M. de Oliveira1,*, Sidiney G. Alves1,†, and Silvio C. Ferreira2,3,‡

  • 1Departamento de Estatística, Física e Matemática, CAP, Universidade Federal de São João del Rei, 36420-000 Ouro Branco, Minas Gerais, Brazil
  • 2Departamento de Física, Universidade Federal de Viçosa, 36570-900 Viçosa, Minas Gerais, Brazil
  • 3National Institute of Science and Technology for Complex Systems, Rio de Janeiro, Brazil

  • *mmdeoliveira@ufsj.edu.br
  • sidiney@ufsj.edu.br
  • silviojr@ufv.br

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Issue

Vol. 100, Iss. 5 — November 2019

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