Dynamics of a Continual Sociological Model

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Dynamics of a Continual Sociological Model. / Pilyugin, S. Yu ; Sabirova, D. Z.

In: Vestnik St. Petersburg University: Mathematics, Vol. 54, No. 2, 04.2021, p. 196-205.

Research output: Contribution to journal › Article › peer-review

Author

Pilyugin, S. Yu ; Sabirova, D. Z. / Dynamics of a Continual Sociological Model. In: Vestnik St. Petersburg University: Mathematics. 2021 ; Vol. 54, No. 2. pp. 196-205.

BibTeX

@article{21b8552b0c744c5b92490ce540dc5d4d,

title = "Dynamics of a Continual Sociological Model",

abstract = "Abstract: In this paper, we study a discrete dynamical system modeling an iterative process of choice in a group of agents between two possible outcomes. The model under study is based on the bounded confidence principle introduced by Hegselmann and Krause. According to this principle, at each step of the process, an agent forms their opinion based on similar opinions of other agents. 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 the application of essentially new research methods. The structure of possible fixed points of the arising dynamical system is described and their stability is studied. It is shown that any trajectory tends to a fixed point.",

keywords = "bounded confidence, dynamical system, fixed point, opinion dynamics, stability",

author = "Pilyugin, {S. Yu} and Sabirova, {D. Z.}",

note = "Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = apr,

doi = "10.1134/S1063454121020102",

language = "English",

volume = "54",

pages = "196--205",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - Dynamics of a Continual Sociological Model

AU - Pilyugin, S. Yu

AU - Sabirova, D. Z.

PY - 2021/4

Y1 - 2021/4

N2 - Abstract: In this paper, we study a discrete dynamical system modeling an iterative process of choice in a group of agents between two possible outcomes. The model under study is based on the bounded confidence principle introduced by Hegselmann and Krause. According to this principle, at each step of the process, an agent forms their opinion based on similar opinions of other agents. 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 the application of essentially new research methods. The structure of possible fixed points of the arising dynamical system is described and their stability is studied. It is shown that any trajectory tends to a fixed point.

AB - Abstract: In this paper, we study a discrete dynamical system modeling an iterative process of choice in a group of agents between two possible outcomes. The model under study is based on the bounded confidence principle introduced by Hegselmann and Krause. According to this principle, at each step of the process, an agent forms their opinion based on similar opinions of other agents. 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 the application of essentially new research methods. The structure of possible fixed points of the arising dynamical system is described and their stability is studied. It is shown that any trajectory tends to a fixed point.

KW - bounded confidence

KW - dynamical system

KW - fixed point

KW - opinion dynamics

KW - stability

UR - http://www.scopus.com/inward/record.url?scp=85108110492&partnerID=8YFLogxK

U2 - 10.1134/S1063454121020102

DO - 10.1134/S1063454121020102

M3 - Article

AN - SCOPUS:85108110492

VL - 54

SP - 196

EP - 205

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -

ID: 92247765