Joint effect of ageing and multilayer structure prevents ordering in the voter model

TL;DR

This study explores how ageing and multilayer network structures influence the voter model's dynamics, revealing a critical multiplexity threshold that determines whether the system reaches consensus or remains trapped in non-absorbing states.

Contribution

It introduces a combined analysis of ageing and multilayer effects on the voter model, identifying a critical multiplexity parameter that alters the system's long-term behavior.

Findings

A critical multiplexity value q* separates different dynamical regimes.

Below q*, the system often gets trapped in non-absorbing states due to ageing.

Above q*, the voter model reliably reaches consensus.

Abstract

The voter model rules are simple, with agents copying the state of a random neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the model has also applications for catalysis and species competition. Inspired by the temporal inhomogeneities found in human interactions, one can introduce ageing in the agents: the probability to update decreases with the time elapsed since the last change. This modified dynamics induces an approach to consensus via coarsening in complex networks. Additionally, multilayer networks produce profound changes in the dynamics of models. In this work, we investigate how a multilayer structure affects the dynamics of an ageing voter model. The system is studied as a function of the fraction of nodes sharing states across layers (multiplexity parameter q ). We find that the dynamics of the system suffers a notable change at an intermediate value q*. Above it, the voter model always orders to an absorbing configuration. While, below, a fraction of the realizations falls into dynamical traps associated to a spontaneous symmetry breaking in which the majority opinion in the different layers takes opposite signs and that due to the ageing indefinitely delay the arrival at the absorbing state.