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ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Convergence of Trajectories and Stability of Fixed Points in a Modified Hegselmann-Krause Model

Author(s):

Nikolay Knyazev

Student of Faculty of Mathematics and Computer Science,
St. Petersburg State University

knyaz03@mail.ru

Sergei Yurievich Pilyugin

Doctor of Physical and Mathematical Sciences, Professor of Faculty
of Mathematics and Computer Science, St. Petersburg State University

sergeipil47@mail.ru

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

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