Generic Absorbing Transition in Coevolution Dynamics

TL;DR

This paper analyzes a coevolution voter model on networks, revealing an absorbing transition from active to frozen phases at a critical rewiring probability, driven by the competition between network and node state evolution.

Contribution

It introduces a mean-field approximation to identify a critical point for the phase transition in coevolving networks based on node states and network structure.

Findings

Critical rewiring probability depends only on average degree.

Transition characterized by diverging time scale at critical point.

Active and frozen phases correspond to connected and fragmented networks.

Abstract

We study a coevolution voter model on a network that evolves according to the state of the nodes. In a single update, a link between opposite-state nodes is rewired with probability $p$, while with probability $1-p$ one of the nodes takes its neighbor's state. A mean-field approximation reveals an absorbing transition from an active to a frozen phase at a critical value $p_c=\frac{\mu-2}{\mu-1}$ that only depends on the average degree $\mu$ of the network. The approach to the final state is characterized by a time scale that diverges at the critical point as $\tau \sim |p_c-p|^{-1}$. We find that the active and frozen phases correspond to a connected and a fragmented network respectively. We show that the transition in finite-size systems can be seen as the sudden change in the trajectory of an equivalent random walk at the critical rewiring rate $p_c$, highlighting the fact that the mechanism behind the transition is a competition between the rates at which the network and the state of the nodes evolve.