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

TL;DR

This paper develops a pairwise mean-field theory for the two-species symbiotic contact process on networks, showing it outperforms standard models in predicting phase transitions and stationary states, validated by simulations.

Contribution

The paper introduces a pairwise mean-field approach that accurately captures dynamical correlations in the 2SCP on various networks, surpassing traditional one-site theories.

Findings

Pairwise theory accurately predicts stationary states on regular networks.

It captures transition points in heterogeneous networks.

The approach reveals complex phase diagrams with new transitions.

Abstract

The two-species symbiotic contact process (2SCP) is a stochastic process where 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 theory 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.