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Generic Absorbing Transition in Coevolution Dynamics
F. Vazquez, V. M. Eguiluz, M. San Miguel
TL;DR
The paper asks how generic fragmentation transitions arise in coevolving networks and studies a voter model coupling state copying with state-dependent rewiring. Mean-field analysis, simulations, and a random-walk representation identify an absorbing transition whose phases correspond to connected and fragmented networks.
Problem
The paper asks how generic network-fragmentation transitions are and which mechanism produces them in systems where interaction topology and node dynamics coevolve.
Method
The authors analyze a coevolution voter model using mean-field equations, numerical simulations, and an equivalent random walk in active-link density and link magnetization.
Results
The model exhibits an absorbing transition from an active phase with a finite active-link density and connected network to a frozen phase with inert links and two disconnected components.
Takeaways & Limitations
The transition results from competition between copying and rewiring dynamics, with their relative rates determining whether the network remains connected or fragments before full ordering.
Abstract
from arXiv · showhide
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 $p_c=\frac{μ-2}{μ-1}$ that only depends on the average degree $μ$ of the network. The approach to the final state is characterized by a time scale that diverges at the critical point as $τ\sim |p_c-p|^{-1}$. 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.