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Accurate mean-field equation for voter model dynamics on scale-free networks
Marvin Lücke1, Stefanie Winkelmann1, Péter Koltai2
1Zuse Institute Berlin, Modeling and Simulation of Complex Processes, Berlin, Germany.
Physical Review. E
|April 18, 2026
Summary
We present a modified mean-field theory for voter model dynamics on scale-free networks. This approach improves accuracy by using degree-weighted shares and a correlation factor, outperforming standard methods.
Area of Science:
- Complex Systems
- Network Science
- Statistical Physics
Background:
- Macroscopic behavior of dynamical systems on networks is challenging to understand.
- Mean-field theory is effective for dense networks but fails on scale-free networks.
Purpose of the Study:
- To introduce a modified mean-field approximation for voter model dynamics on scale-free networks.
- To improve the accuracy of macroscopic models for realistic network structures.
Main Methods:
- Modified mean-field approximation using degree-weighted shares.
- Incorporation of a correlation factor to account for interactions.
Main Results:
- The correlation factor is a network property, independent of state or process parameters.
- The modified approach significantly reduces approximation error compared to standard methods.
Conclusions:
- The proposed method enhances the predictive power of mean-field theory for scale-free networks.
- This approach offers a more accurate and efficient way to model complex systems on realistic networks.
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