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Bistability and multistability in opinion dynamics models

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  • 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
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    References listed on IDEAS

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    Cited by:

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    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).
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    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).

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