Symmetry-Breaking and Hysteresis in a Duplex Voter Model

Christian Kluge; Christian Kuehn

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arXiv · 2604.05860

Symmetry-Breaking and Hysteresis in a Duplex Voter Model

Christian Kluge·Christian Kuehn

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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.

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Christian Kluge, Christian Kuehn. 2026-04-07. Symmetry-Breaking and Hysteresis in a Duplex Voter Model. https://arxiv.org/abs/2604.05860

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