An accurate mean-field equation for voter model dynamics on scale-free networks
under review
- 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 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.
| Author: | Marvin Lücke, Stefanie WinkelmannORCiD, Peter Koltai |
|---|---|
| Document Type: | Article |
| Year of first publication: | 2025 |
| ArXiv Id: | http://arxiv.org/abs/2509.13485 |

