Symmetry-Breaking and Hysteresis in a Duplex Voter Model
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908943908864000 |
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| author | Kluge, Christian Kuehn, Christian |
| author_facet | Kluge, Christian Kuehn, Christian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05860 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetry-Breaking and Hysteresis in a Duplex Voter Model Kluge, Christian Kuehn, Christian Adaptation and Self-Organizing Systems Dynamical Systems Physics and Society 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. |
| title | Symmetry-Breaking and Hysteresis in a Duplex Voter Model |
| topic | Adaptation and Self-Organizing Systems Dynamical Systems Physics and Society |
| url | https://arxiv.org/abs/2604.05860 |