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Opinion dynamics as a movement in a bistable potential

Author

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  • Nyczka, Piotr
  • Cisło, Jerzy
  • Sznajd-Weron, Katarzyna

Abstract

In this paper, we investigate the Sznajd model of opinion dynamics with anticonformity on a complete graph. We show that below some threshold value of anticonformal behavior spontaneous reorientations occur between two stable states. Dealing with a complete graph allows us also for an analytical treatment. We provide analytical calculations both for the infinite and finite systems. We show that opinion dynamics can be understood as a movement of a public opinion in a symmetric bistable effective potential. We focus also on the spontaneous transitions between stable states in the case of the finite system and show that a typical waiting time can be observed.

Suggested Citation

  • Nyczka, Piotr & Cisło, Jerzy & Sznajd-Weron, Katarzyna, 2012. "Opinion dynamics as a movement in a bistable potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 317-327.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:1:p:317-327
    DOI: 10.1016/j.physa.2011.07.050
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    Citations

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    Cited by:

    1. Sznajd-Weron, Katarzyna & Sznajd, Józef & Weron, Tomasz, 2021. "A review on the Sznajd model — 20 years after," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    2. Wang, Shaoli & Rong, Libin & Wu, Jianhong, 2016. "Bistability and multistability in opinion dynamics models," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 388-395.
    3. Calvelli, Matheus & Crokidakis, Nuno & Penna, Thadeu J.P., 2019. "Phase transitions and universality in the Sznajd model with anticonformity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 518-523.
    4. Qesmi, Redouane, 2021. "Hopf bifurcation in an opinion model with state-dependent delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    5. Bartłomiej Nowak & Katarzyna Sznajd-Weron, 2019. "Homogeneous Symmetrical Threshold Model with Nonconformity: Independence versus Anticonformity," Complexity, Hindawi, vol. 2019, pages 1-14, April.
    6. Takano, Masanori & Nakazato, Kenichi & Taka, Fumiaki, 2023. "Dynamics of discrimination and prejudice via two types of social contagion," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    7. Qesmi, Redouane, 2021. "Dynamics of an opinion model with threshold-type delay," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. Muslim, Roni & Wella, Sasfan A. & Nugraha, Ahmad R.T., 2022. "Phase transition in the majority rule model with the nonconformist agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P2).

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