Accurate mean-field equation for voter model dynamics on scale-free networks
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912971659149312 |
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| author | Lücke, Marvin Winkelmann, Stefanie Koltai, Péter |
| author_facet | Lücke, Marvin Winkelmann, Stefanie Koltai, Péter |
| contents | Understanding the emergent macroscopic behavior of dynamical systems on networks is a crucial but challenging task. One of the simplest and most effective methods to construct a reduced macroscopic model is given by mean-field theory. The resulting approximations perform well on dense and homogeneous networks but poorly on scale-free networks, which, however, are more realistic in many applications. In this paper, we introduce a modified version of the mean-field approximation for voter model dynamics on scale-free networks. The two main deviations from classical theory are that we use degree-weighted shares as coarse variables and that we introduce a correlation factor that can be interpreted as slowing down dynamics induced by interactions. We observe that, for moderate noise and comparable interaction rates, the correlation factor is only a property of the network and not of the state or of parameters of the process. This approach achieves a significantly smaller approximation error than standard methods without increasing dimensionality. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_13485 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Accurate mean-field equation for voter model dynamics on scale-free networks Lücke, Marvin Winkelmann, Stefanie Koltai, Péter Physics and Society Understanding the emergent macroscopic behavior of dynamical systems on networks is a crucial but challenging task. One of the simplest and most effective methods to construct a reduced macroscopic model is given by mean-field theory. The resulting approximations perform well on dense and homogeneous networks but poorly on scale-free networks, which, however, are more realistic in many applications. In this paper, we introduce a modified version of the mean-field approximation for voter model dynamics on scale-free networks. The two main deviations from classical theory are that we use degree-weighted shares as coarse variables and that we introduce a correlation factor that can be interpreted as slowing down dynamics induced by interactions. We observe that, for moderate noise and comparable interaction rates, the correlation factor is only a property of the network and not of the state or of parameters of the process. This approach achieves a significantly smaller approximation error than standard methods without increasing dimensionality. |
| title | Accurate mean-field equation for voter model dynamics on scale-free networks |
| topic | Physics and Society |
| url | https://arxiv.org/abs/2509.13485 |