Voter-like Dynamics with Conflicting Preferences on Modular Networks
Abstract
:1. Introduction
1.1. Literature Review
1.2. Contributions and Article Structure
2. Model
- One node (agent) i is selected uniformly randomly.
- A neighbor j of node i is selected uniformly randomly.
- If i and j have opposite opinions, i takes the opinion of j with probability . Otherwise, nothing happens.
- Repeat the process until consensus or apparent stabilization is reached.
3. Results
3.1. Fully Connected Network
- The positive (all up spins) and negative (all down spins) consensus points are always fixed points, for any combination of the parameters .
- When the positive (or negative) consensus is stable, it is the only stable fixed point.
- When both the consensus fixed points are not stable, another fixed point with appears. Such a fixed point, when it exists, is always stable.
3.2. Modular Networks
3.3. Pair Approximation
3.4. Application to the Network of Blogs
4. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ODEs | Ordinary Differential Equations |
Appendix A. Linear Stability Analysis
Appendix A.1. Fully Connected Network
Appendix A.2. Modular Networks
Appendix B. Mean-Field Transition Rates for Modular Networks
Appendix C. Derivation of the Pair Approximation System of ODEs
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Zimmaro, F.; Contucci, P.; Kertész, J. Voter-like Dynamics with Conflicting Preferences on Modular Networks. Entropy 2023, 25, 838. https://doi.org/10.3390/e25060838
Zimmaro F, Contucci P, Kertész J. Voter-like Dynamics with Conflicting Preferences on Modular Networks. Entropy. 2023; 25(6):838. https://doi.org/10.3390/e25060838
Chicago/Turabian StyleZimmaro, Filippo, Pierluigi Contucci, and János Kertész. 2023. "Voter-like Dynamics with Conflicting Preferences on Modular Networks" Entropy 25, no. 6: 838. https://doi.org/10.3390/e25060838