Consensus and clustering in opinion formation on networks.
| Autor: | Bujalski J; Department of Mathematics, Emmanuel College, Boston, MA 02115, USA., Dwyer G; Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA., Kapitula T; Department of Mathematics and Statistics, Calvin College, Grand Rapids, MI 49546, USA tmk5@calvin.edu., Le QN; Division of Applied Mathematics and ICERM, Providence, RI 02912, USA., Malvai H; Division of Applied Mathematics and ICERM, Providence, RI 02912, USA., Rosenthal-Kay J; Booth School of Business, University of Chicago, Chicago, IL 60637, USA., Ruiter J; Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA. |
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| Jazyk: | angličtina |
| Zdroj: | Philosophical transactions. Series A, Mathematical, physical, and engineering sciences [Philos Trans A Math Phys Eng Sci] 2018 Apr 13; Vol. 376 (2117). |
| DOI: | 10.1098/rsta.2017.0186 |
| Abstrakt: | Ideas that challenge the status quo either evaporate or dominate. The study of opinion dynamics in the socio-physics literature treats space as uniform and considers individuals in an isolated community, using ordinary differential equation (ODE) models. We extend these ODE models to include multiple communities and their interactions. These extended ODE models can be thought of as being ODEs on directed graphs. We study in detail these models to determine conditions under which there will be consensus and pluralism within the system. Most of the consensus/pluralism analysis is done for the case of one and two cities. However, we numerically show for the case of a symmetric cycle graph that an elementary bifurcation analysis provides insight into the phenomena of clustering. Moreover, for the case of a cycle graph with a hub, we discuss how having a sufficient proportion of zealots in the hub leads to the entire network sharing the opinion of the zealots.This article is part of the theme issue 'Stability of nonlinear waves and patterns and related topics'. (© 2018 The Author(s).) |
| Databáze: | MEDLINE |
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