TY - JOUR

T1 - Convergence to Fixed Points in One Model of Opinion Dynamics

AU - Bodunov, Nikolai A.

AU - Pilyugin, Sergei Yu

N1 - Publisher Copyright: © 2020, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2021

Y1 - 2021

N2 - In this paper, we study the limit behavior of trajectories of a nonlinear and discontinuous model of opinion dynamics based on the notion of bounded confidence. This model was previously studied in the case where the influence function has the form i(v) = v. It was shown that, under a particular condition on parameters of the system, any its trajectory tends to a fixed point. In this paper, we prove a similar result under weaker conditions on the influence function: it is assumed that i(v) is continuous, nonstrictly increasing, and i(v) = 0 if and only if v = 0.

AB - In this paper, we study the limit behavior of trajectories of a nonlinear and discontinuous model of opinion dynamics based on the notion of bounded confidence. This model was previously studied in the case where the influence function has the form i(v) = v. It was shown that, under a particular condition on parameters of the system, any its trajectory tends to a fixed point. In this paper, we prove a similar result under weaker conditions on the influence function: it is assumed that i(v) is continuous, nonstrictly increasing, and i(v) = 0 if and only if v = 0.

KW - Bounded confidence

KW - Dynamical system

KW - Fixed point

KW - Opinion dynamics

UR - http://www.scopus.com/inward/record.url?scp=85091917215&partnerID=8YFLogxK

U2 - 10.1007/s10883-020-09514-1

DO - 10.1007/s10883-020-09514-1

M3 - Article

AN - SCOPUS:85091917215

VL - 27

SP - 617

EP - 623

JO - Journal of Dynamical and Control Systems

JF - Journal of Dynamical and Control Systems

SN - 1079-2724

ER -