Detecting and Describing Dynamic Equilibria in Adaptive Networks

TL;DR

This paper reviews models of the contact process on adaptive networks, analyzing how different rewiring mechanisms influence the steady-state network topology and dynamics.

Contribution

It introduces an extended framework for detecting active stationary states across various adaptive network models and analyzes the impact of rewiring rule modifications.

Findings

Rewiring rules significantly affect steady-state topologies.

A coarse-grained view of coevolving networks is developed.

Different rewiring schemes lead to diverse steady-state statistics.

Abstract

We review modeling attempts for the paradigmatic contact process (or SIS model) on adaptive networks. Elaborating on one particular proposed mechanism of topology change (rewiring) and its mean field analysis, we obtain a coarse-grained view of coevolving network topology in the stationary active phase of the system. Introducing an alternative framework applicable to a wide class of adaptive networks, active stationary states are detected, and an extended description of the resulting steady-state statistics is given for three different rewiring schemes. We find that slight modifications of the standard rewiring rule can result in either minuscule or drastic change of steady-state network topologies.