Phase transitions for polyadic epidemic and voter models with multiscale groups
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915544056201216 |
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| author | Steinmeyer, Pia Mölter, Jan Kuehn, Christian |
| author_facet | Steinmeyer, Pia Mölter, Jan Kuehn, Christian |
| contents | Polyadic (or higher-order) interactions can significantly impact the dynamics of interacting particle systems. However, previous studies have often assumed group sizes to be relatively small. In this work, we examine the influence of multiscale polyadic group interactions, where some groups are small and others are very large. We consider two paradigmatic examples, an SIS-epidemic and the adaptive voter model. On the level of the mean field, we specifically discuss the impact of the multiscale polyadic interactions on equilibrium dynamics and phase transitions. For the SIS-epidemic model, we find a region of bistability that protects the disease-free state over a wide range beyond the classical epidemic threshold from a significant outbreak. For the adaptive voter model, we show that multiscale polyadic interactions can stabilize the network or increase the convergence rate to an unbiased equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12682 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phase transitions for polyadic epidemic and voter models with multiscale groups Steinmeyer, Pia Mölter, Jan Kuehn, Christian Adaptation and Self-Organizing Systems Physics and Society Polyadic (or higher-order) interactions can significantly impact the dynamics of interacting particle systems. However, previous studies have often assumed group sizes to be relatively small. In this work, we examine the influence of multiscale polyadic group interactions, where some groups are small and others are very large. We consider two paradigmatic examples, an SIS-epidemic and the adaptive voter model. On the level of the mean field, we specifically discuss the impact of the multiscale polyadic interactions on equilibrium dynamics and phase transitions. For the SIS-epidemic model, we find a region of bistability that protects the disease-free state over a wide range beyond the classical epidemic threshold from a significant outbreak. For the adaptive voter model, we show that multiscale polyadic interactions can stabilize the network or increase the convergence rate to an unbiased equilibrium. |
| title | Phase transitions for polyadic epidemic and voter models with multiscale groups |
| topic | Adaptation and Self-Organizing Systems Physics and Society |
| url | https://arxiv.org/abs/2410.12682 |