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Dynamics of an opinion model with threshold-type delay

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  • Qesmi, Redouane

Abstract

The process of opinion formation rarely boils down to accepting or rejecting the social consensus of others, despite the considerable research (since Sch, 1956 [5]) that has been focused on such situations. In this paper, we propose a mathematical model of threshold-type delay differential equations describing the relationship between two subpopulations with opposite opinions and the opinion spread dynamics. We study the quantitative as well as qualitative properties of our model, and we present results on positivity and boundedness, local stability of equilibria and global stability of the boundary state under certain conditions. Further analysis of the model show that the system exhibits either a forward transcritical or a backward bifurcation. Furthermore, numerical simulations and sensitivity analysis are performed to study the impact of the relevant parameters of the model on the achievement of the consensus.

Suggested Citation

  • Qesmi, Redouane, 2021. "Dynamics of an opinion model with threshold-type delay," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920307736
    DOI: 10.1016/j.chaos.2020.110379
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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.
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    3. Dustin L. Arendt & Leslie M. Blaha, 2015. "Opinions, influence, and zealotry: a computational study on stubbornness," Computational and Mathematical Organization Theory, Springer, vol. 21(2), pages 184-209, June.
    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. Galam, Serge, 1999. "Application of statistical physics to politics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 132-139.
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