 Hopf bifurcation in an opinion model with state-dependent delayRedouane Qesmi Chaos, Solitons & Fractals, 2021, vol. 153, issue P2 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. Keywords: Opinion; Functional differential equation; State-dependent delay; Hopf bifurcation; Periodic solution (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008651 DOI: 10.1016/j.chaos.2021.111511 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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