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Hopf bifurcation in an opinion model with state-dependent delay

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  • Qesmi, Redouane

Abstract

In a recent paper [R. Qesmi, Dynamics of an opinion model with threshold-type delay, Chaos, Solitons & Fractals 98 (2020). (https://doi.org/10.1016/j.chaos.2020.110379)], we proposed a mathematical model of threshold-type delay differential equations describing the relationship between two subpopulations with opposite opinions and the opinion spread dynamics. The study there showed the possibility of a transcritical forward and backward bifurcations of positive equilibria. In the present paper, we show that the opinion model undergoes a Hopf bifurcation through which one of the bifurcation branches loses the stability and periodic solutions appear. One of the important consequences of the obtained dynamics is that the consensus of the both opinions could be lost by maintaining the balance between the time taken for an individual to become convinced of the outsider opinion, which need be short, and the number of individuals converted to the local opinion which need be low. Finally, we provide numerical simulations to illustrate and support our theoretical results.

Suggested Citation

  • Qesmi, Redouane, 2021. "Hopf bifurcation in an opinion model with state-dependent delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008651
    DOI: 10.1016/j.chaos.2021.111511
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    References listed on IDEAS

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    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. Pablo Balenzuela & Juan Pablo Pinasco & Viktoriya Semeshenko, 2015. "The Undecided Have the Key: Interaction-Driven Opinion Dynamics in a Three State Model," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-21, October.
    3. M. Fabiana Laguna & Guillermo Abramson & J. Iglesias, 2013. "Compelled to do the right thing," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(5), pages 1-8, May.
    4. 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.
    5. Crokidakis, Nuno, 2012. "Effects of mass media on opinion spreading in the Sznajd sociophysics model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1729-1734.
    6. Juan Carlos González-Avella & Mario G Cosenza & Maxi San Miguel, 2012. "A Model for Cross-Cultural Reciprocal Interactions through Mass Media," PLOS ONE, Public Library of Science, vol. 7(12), pages 1-7, December.
    7. Pinasco, Juan Pablo & Semeshenko, Viktoriya & Balenzuela, Pablo, 2017. "Modeling opinion dynamics: Theoretical analysis and continuous approximation," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 210-215.
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