Convergence of trajectories and stability of fixed points in a modified Hegselmann - Krause model

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Convergence of trajectories and stability of fixed points in a modified Hegselmann - Krause model. / Пилюгин, Сергей Юрьевич ; Князев, Николай Даниилович.

в: ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ, № 4, 12.2024, стр. 53-77.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{0ddbabbf7b6f43cab5328103ed75c6b8,

title = "Convergence of trajectories and stability of fixed points in a modified Hegselmann - Krause model",

abstract = "In this paper, we study a modified Hegselmann - Krause model of opinion dynamics based on the bounded confidence principle.This model is formulated as a discontinuous and nonlinear dynamical system. At any time moment of the process of opinion formation,the operator of forming the next opinion of an agent is two-step; first, one takes the average of opinions of agents sharing similar opinions plus his/her own; in the second step, a regularization procedure is performed. A new regularization procedure is applied. We find conditions under which every trajectory tends to a fixed point of the system and study stability properties of fixed points.",

keywords = "Opinion dynamics, bounded confidence principle, Hegselmann - Krause model, convergence of trajectories, stability of fixed points",

author = "Пилюгин, {Сергей Юрьевич} and Князев, {Николай Даниилович}",

year = "2024",

month = dec,

language = "English",

pages = "53--77",

journal = "ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ",

issn = "1817-2172",

publisher = "Электронный журнал {"}Дифференциальные уравнения и процессы управления{"}",

number = "4",

}

RIS

TY - JOUR

T1 - Convergence of trajectories and stability of fixed points in a modified Hegselmann - Krause model

AU - Пилюгин, Сергей Юрьевич

AU - Князев, Николай Даниилович

PY - 2024/12

Y1 - 2024/12

N2 - In this paper, we study a modified Hegselmann - Krause model of opinion dynamics based on the bounded confidence principle.This model is formulated as a discontinuous and nonlinear dynamical system. At any time moment of the process of opinion formation,the operator of forming the next opinion of an agent is two-step; first, one takes the average of opinions of agents sharing similar opinions plus his/her own; in the second step, a regularization procedure is performed. A new regularization procedure is applied. We find conditions under which every trajectory tends to a fixed point of the system and study stability properties of fixed points.

AB - In this paper, we study a modified Hegselmann - Krause model of opinion dynamics based on the bounded confidence principle.This model is formulated as a discontinuous and nonlinear dynamical system. At any time moment of the process of opinion formation,the operator of forming the next opinion of an agent is two-step; first, one takes the average of opinions of agents sharing similar opinions plus his/her own; in the second step, a regularization procedure is performed. A new regularization procedure is applied. We find conditions under which every trajectory tends to a fixed point of the system and study stability properties of fixed points.

KW - Opinion dynamics, bounded confidence principle, Hegselmann - Krause model, convergence of trajectories, stability of fixed points

M3 - Article

SP - 53

EP - 77

JO - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1817-2172

IS - 4

ER -

ID: 126280597