Accurate mean-field equation for voter model dynamics on scale-free networks

Titelangaben

Lücke, Marvin ; Winkelmann, Stefanie ; Koltai, Peter:
Accurate mean-field equation for voter model dynamics on scale-free networks.
In: Physical Review E. Bd. 113 (2026) . - 034311.
ISSN 2470-0053
DOI: https://doi.org/10.1103/vkpx-5cvt

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Abstract

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.