Symmetry-Breaking and Hysteresis in a Duplex Voter Model

TL;DR

This paper introduces a two-layer multiplex voter model exhibiting complex phase behavior, including symmetry-breaking and bifurcations, with analytical and numerical validation.

Contribution

It presents a novel multiplex voter model demonstrating rich phase transitions and bifurcations, expanding understanding of symmetry-breaking in network dynamics.

Findings

Reveals a phase diagram with spontaneous symmetry-breaking.

Identifies a cusp bifurcation induced by noise.

Shows the model's relation to explosive transition phenomena.

Abstract

We introduce and analyze a voter-type model on a two-layer multiplex network, where the presence of a state on one layer acts as a catalyst or inhibitor to the propagation of that state on the other layer. Despite the model's simplicity, our mathematical analysis reveals a rich phase diagram that includes spontaneous symmetry-breaking and a cusp bifurcation, which arises when noise is introduced into the model. In particular, this bifurcation mechanism can be viewed as a prototypical unfolding of the change between explosive and non-explosive transitions observed in various other network models. We cross-validate our analytic results by numerical simulations.