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This article is cited in 1 scientific paper (total in 1 paper)
MATHEMATICS
Dynamics of one continual sociological model
S. Yu. Pilyugin, D. Z. Sabirova St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Abstract:
In this paper, we study a dynamical system modeling an iterative process of choice in a group of agents between two possible results. The studied model is based on the principle of bounded confidence introduced by Hegselmann and Krause. According to this principle, at each step of the process, any agent chaqnges his/her opinion being influenced by agents with close opinions. The resulting dynamical system is nonlinear and discontinuous. The principal novelty of the model studied in this paper is that we consider not a finite but an infinite (continual) group of agents. Such an approach requires application of essentially new methods of research. The structure of possible fixed points of the appearing dynamical system is described, their stability is studied. It is shown that any trajectory tends to a fixed point.
Keywords:
dynamical system, opinion dynamics, bounded confidence, fixed point, stability.
Received: 24.03.2020 Revised: 16.11.2020 Accepted: 17.12.2020
Citation:
S. Yu. Pilyugin, D. Z. Sabirova, “Dynamics of one continual sociological model”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8:2 (2021), 317–330; Vestn. St. Petersbg. Univ., Math., 8:3 (2021), 196–205
Linking options:
https://www.mathnet.ru/eng/vspua118 https://www.mathnet.ru/eng/vspua/v8/i2/p317
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