Symmetry-Breaking and Hysteresis in a Duplex Voter Model

2026/04/07 by Christian Kluge, Christian Kuehn · 1 voice
Physics and Astronomy · Mathematics · #nlin.AO #math.DS #physics.soc-ph

paper · pdf

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.

Citations

• Multilayer network science: theory, methods, and applications
• Multilayer coevolution dynamics of the nonlinear voter model
• Reality Inspired Voter Models: A Mini-Review
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• Moment Closure - A Brief Review
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• Dynamics of interacting diseases
• Multilayer Networks
• Moment-Closure Approximations for Discrete Adaptive Networks
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• Voter models on heterogeneous networks
• Evolutionary dynamics on degree-heterogeneous graphs
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Discussions

• Christian Kluge, Christian Kuehn: Symmetry-Breaking and Hysteresis in a Duplex Voter Model https://arxiv.org/abs/2604.05860 https://arxiv.org/pdf/2604.05860 https://arxiv.org/html/2604.05860 [bsky, 0 points, 0 comments]

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