IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v289y2016icp388-395.html
   My bibliography  Save this article

Bistability and multistability in opinion dynamics models

Author

Listed:
  • Wang, Shaoli
  • Rong, Libin
  • Wu, Jianhong

Abstract

In this paper, we analyze a few opinion formation or election game dynamics models. For a simple model with two subpopulations with opposing opinions A and B, if the fraction of committed believers of opinion A (“A zealots”) is less than a critical value, then the system has two bistable equilibrium points. When the fraction is equal to the critical value, the system undergoes a saddle-node bifurcation. When the fraction is larger than the critical value, a boundary equilibrium point is globally asymptotically stable, suggesting that the entire population reaches a consensus on A. We find a similar bistability property in the model in which both opinions have their own zealots. We also extend the model to include multiple competitors and show the dynamical behavior of multistability. The more competitors subpopulation A has, the fewer zealots opinion A needs to obtain consensus.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:289:y:2016:i:c:p:388-395
    DOI: 10.1016/j.amc.2016.05.030
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316303393
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.05.030?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. C. J. Tessone & R. Toral, 2004. "Neighborhood models of minority opinion spreading," Computing in Economics and Finance 2004 206, Society for Computational Economics.
    3. Wu, Fang & Huberman, Bernardo A. & Adamic, Lada A. & Tyler, Joshua R., 2004. "Information flow in social groups," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(1), pages 327-335.
    4. Grzegorz Kondrat & Katarzyna Sznajd-Weron, 2010. "Spontaneous Reorientations In A Model Of Opinion Dynamics With Anticonformists," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 559-566.
    5. Rainer Hegselmann & Ulrich Krause, 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(3), pages 1-2.
    6. AskariSichani, Omid & Jalili, Mahdi, 2015. "Influence maximization of informed agents in social networks," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 229-239.
    7. Mohammad Afshar & Masoud Asadpour, 2010. "Opinion Formation by Informed Agents," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 13(4), pages 1-5.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Monteiro, L.H.A., 2019. "A discrete-time dynamical system with four types of codimension-one bifurcations," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 189-191.
    2. Han, Wenchen & Feng, Yuee & Qian, Xiaolan & Yang, Qihui & Huang, Changwei, 2020. "Clusters and the entropy in opinion dynamics on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    3. Lachowicz, Mirosław & Leszczyński, Henryk & Topolski, Krzysztof A., 2019. "Self-organization with small range interactions: Equilibria and creation of bipolarity," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 156-166.
    4. Qesmi, Redouane, 2021. "Dynamics of an opinion model with threshold-type delay," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Kareeva, Yulia & Sedakov, Artem & Zhen, Mengke, 2023. "Influence in social networks with stubborn agents: From competition to bargaining," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    6. Qesmi, Redouane, 2021. "Hopf bifurcation in an opinion model with state-dependent delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    7. Charcon, D.Y. & Monteiro, L.H.A., 2020. "A multi-agent system to predict the outcome of a two-round election," Applied Mathematics and Computation, Elsevier, vol. 386(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fan, Kangqi & Pedrycz, Witold, 2016. "Opinion evolution influenced by informed agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 431-441.
    2. Evangelos Ioannidis & Nikos Varsakelis & Ioannis Antoniou, 2020. "Promoters versus Adversaries of Change: Agent-Based Modeling of Organizational Conflict in Co-Evolving Networks," Mathematics, MDPI, vol. 8(12), pages 1-25, December.
    3. AskariSichani, Omid & Jalili, Mahdi, 2015. "Influence maximization of informed agents in social networks," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 229-239.
    4. Rusinowska, Agnieszka & Taalaibekova, Akylai, 2019. "Opinion formation and targeting when persuaders have extreme and centrist opinions," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 9-27.
    5. Ghezelbash, Ehsan & Yazdanpanah, Mohammad Javad & Asadpour, Masoud, 2019. "Polarization in cooperative networks through optimal placement of informed agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    6. Quanbo Zha & Gang Kou & Hengjie Zhang & Haiming Liang & Xia Chen & Cong-Cong Li & Yucheng Dong, 2020. "Opinion dynamics in finance and business: a literature review and research opportunities," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-22, December.
    7. 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.
    8. Jalili, Mahdi, 2013. "Social power and opinion formation in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 959-966.
    9. Han, Wenchen & Gao, Shun & Huang, Changwei & Yang, Junzhong, 2022. "Non-consensus states in circular opinion model with repulsive interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    10. Balankin, Alexander S. & Martínez Cruz, Miguel Ángel & Martínez, Alfredo Trejo, 2011. "Effect of initial concentration and spatial heterogeneity of active agent distribution on opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3876-3887.
    11. Fang Wu & Bernardo A. Huberman, 2004. "Social Structure and Opinion Formation," Computational Economics 0407002, University Library of Munich, Germany.
    12. Han, Wenchen & Feng, Yuee & Qian, Xiaolan & Yang, Qihui & Huang, Changwei, 2020. "Clusters and the entropy in opinion dynamics on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    13. Yan, Fuhan & Li, Zhaofeng & Jiang, Yichuan, 2016. "Controllable uncertain opinion diffusion under confidence bound and unpredicted diffusion probability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 85-100.
    14. Alireza Mansouri & Fattaneh Taghiyareh, 2020. "Phase Transition in the Social Impact Model of Opinion Formation in Scale-Free Networks: The Social Power Effect," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 23(2), pages 1-3.
    15. 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).
    16. David Anzola & Peter Barbrook-Johnson & Juan I. Cano, 2017. "Self-organization and social science," Computational and Mathematical Organization Theory, Springer, vol. 23(2), pages 221-257, June.
    17. Bartłomiej Nowak & Katarzyna Sznajd-Weron, 2019. "Homogeneous Symmetrical Threshold Model with Nonconformity: Independence versus Anticonformity," Complexity, Hindawi, vol. 2019, pages 1-14, April.
    18. 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).
    19. Yaofeng Zhang & Renbin Xiao, 2015. "Modeling and Simulation of Polarization in Internet Group Opinions Based on Cellular Automata," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-15, August.
    20. Deffuant, Guillaume & Huet, Sylvie, 2007. "Propagation effects of filtering incongruent information," Journal of Business Research, Elsevier, vol. 60(8), pages 816-825, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:289:y:2016:i:c:p:388-395. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.