Competition between group interactions and nonlinearity in voter dynamics on hypergraphs
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912138341122048 |
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| author | Kim, Jihye Lee, Deok-Sun Min, Byungjoon Porter, Mason A. Miguel, Maxi San Goh, K. -I. |
| author_facet | Kim, Jihye Lee, Deok-Sun Min, Byungjoon Porter, Mason A. Miguel, Maxi San Goh, K. -I. |
| contents | Social dynamics are often driven by both pairwise (i.e., dyadic) relationships and higher-order (i.e., polyadic) group relationships, which one can describe using hypergraphs. To gain insight into the impact of polyadic relationships on dynamical processes on networks, we formulate and study a polyadic voter process, which we call the group-driven voter model (GVM), that incorporates the effect of group interactions by nonlinear interactions that are subject to a group (i.e., hyperedge) constraint. By examining the competition between nonlinearity and group sizes, we show that the GVM achieves consensus faster than standard voter-model dynamics, with an optimal minimizing exit time. We substantiate this finding by using mean-field theory on annealed uniform hypergraphs with $N$ nodes, for which the exit time scales as ${\cal A}\ln N$, where the prefactor ${\cal A}$ depends both on the nonlinearity and on group-constraint factors. Our results reveal how competition between group interactions and nonlinearity shapes GVM dynamics. We thereby highlight the importance of such competing effects in complex systems with polyadic interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11261 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Competition between group interactions and nonlinearity in voter dynamics on hypergraphs Kim, Jihye Lee, Deok-Sun Min, Byungjoon Porter, Mason A. Miguel, Maxi San Goh, K. -I. Physics and Society Social and Information Networks Dynamical Systems Adaptation and Self-Organizing Systems Social dynamics are often driven by both pairwise (i.e., dyadic) relationships and higher-order (i.e., polyadic) group relationships, which one can describe using hypergraphs. To gain insight into the impact of polyadic relationships on dynamical processes on networks, we formulate and study a polyadic voter process, which we call the group-driven voter model (GVM), that incorporates the effect of group interactions by nonlinear interactions that are subject to a group (i.e., hyperedge) constraint. By examining the competition between nonlinearity and group sizes, we show that the GVM achieves consensus faster than standard voter-model dynamics, with an optimal minimizing exit time. We substantiate this finding by using mean-field theory on annealed uniform hypergraphs with $N$ nodes, for which the exit time scales as ${\cal A}\ln N$, where the prefactor ${\cal A}$ depends both on the nonlinearity and on group-constraint factors. Our results reveal how competition between group interactions and nonlinearity shapes GVM dynamics. We thereby highlight the importance of such competing effects in complex systems with polyadic interactions. |
| title | Competition between group interactions and nonlinearity in voter dynamics on hypergraphs |
| topic | Physics and Society Social and Information Networks Dynamical Systems Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2407.11261 |