Noise in Coevolving Networks

TL;DR

This paper investigates how different types of noise affect the phase transitions in coevolving networks, revealing that noise can either destroy or modify these transitions.

Contribution

It introduces and analyzes the impact of two distinct noise types on the coevolving voter model's phase transitions, providing analytical support.

Findings

Homogeneous noise destroys the absorbing-fragmentation transition.

Targeted noise preserves transitions but causes shattered fragmentation.

Analytical approximations support the observed effects.

Abstract

Coupling dynamics of the states of the nodes of a network to the dynamics of the network topology leads to generic absorbing and fragmentation transitions. The coevolving voter model is a typical system that exhibits such transitions at some critical rewiring. We study the robustness of these transitions under two distinct ways of introducing noise. Noise affecting all the nodes destroys the absorbing-fragmentation transition, giving rise in finite-size systems to two regimes: bimodal magnetisation and dynamic fragmentation. Noise Targeting a fraction of nodes preserves the transitions but introduces shattered fragmentation with its characteristic fraction of isolated nodes and one or two giant components. Both the lack of absorbing state for homogenous noise and the shift in the absorbing transition to higher rewiring for targeted noise are supported by analytical approximations.