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Boundary effects in a three-state modified voter model for languages

Author

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  • Hadzibeganovic, T.
  • Stauffer, D.
  • Schulze, C.

Abstract

The standard three-state voter model is extended by including the outside pressure favouring one of the three language choices and by adding some biased internal noise. The Monte Carlo simulations are motivated by states with the population divided into three groups of various affinities to each other. We show the crucial influence of the boundaries for moderate lattice sizes like 500×500. By removing the fixed boundary at one side, we demonstrate that this can lead to the victory of one single choice. Noise in contrast stabilizes the choices of all three populations. In addition, we compute the persistence probability, i.e., the number of sites who have never changed their opinion during the simulation, and we consider the case of “rigid-minded” decision makers.

Suggested Citation

  • Hadzibeganovic, T. & Stauffer, D. & Schulze, C., 2008. "Boundary effects in a three-state modified voter model for languages," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3242-3252.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:13:p:3242-3252
    DOI: 10.1016/j.physa.2008.02.003
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    Citations

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    Cited by:

    1. Tanzhe Tang & Caspar G. Chorus, 2019. "Learning Opinions by Observing Actions: Simulation of Opinion Dynamics Using an Action-Opinion Inference Model," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 22(3), pages 1-2.
    2. Michael Boissonneault & Paul Vogt, 2021. "A systematic and interdisciplinary review of mathematical models of language competition," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-12, December.
    3. Takahashi, Takuya & Ihara, Yasuo, 2022. "Application of a Markovian ancestral model to the temporal and spatial dynamics of cultural evolution on a population network," Theoretical Population Biology, Elsevier, vol. 143(C), pages 14-29.
    4. Patriarca, Marco & Heinsalu, Els, 2009. "Influence of geography on language competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(2), pages 174-186.
    5. Zhong, Li-Xin & Xu, Wen-Juan & Chen, Rong-Da & Zhong, Chen-Yang & Qiu, Tian & Shi, Yong-Dong & Wang, Li-Liang, 2016. "A generalized voter model with time-decaying memory on a multilayer network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 95-105.
    6. Hadzibeganovic, Tarik & Stauffer, Dietrich & Han, Xiao-Pu, 2018. "Interplay between cooperation-enhancing mechanisms in evolutionary games with tag-mediated interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 676-690.

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    Keywords

    Monte Carlo simulation; Opinion dynamics;

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