Dynamics of one continual sociological model
DOI:
https://doi.org/10.21638/spbu01.2021.211Abstract
In this paper, we study a dynamical system modeling an iterative process of choice in a group of agents between two possible results. The studied model is based on the principle of bounded confidence introduced by Hegselmann and Krause. According to this principle, at each step of the process, any agent chaqnges his/her opinion being influenced by agents with close opinions. 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 application of essentially new methods of research. The structure of possible fixed points of the appearing dynamical system is described, their stability is studied. It is shown that any trajectory tends to a fixed point.Keywords:
dynamical system, opinion dynamics, bounded confidence, fixed point, stability
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References
Литература
1. Ren W., Cao Y. Distributed Coordination of Multi-agent Networks. Emergent Problems, Models, and Issues. New York, Springer (2011).
2. Krause U. Positive Dynamical Systems in Discrete Time. Theory, Models, and Applications. In: De Gruyter Studies in Mathematics. Vol. 62. Berlin, De Gruyter (2015). https://doi.org/10.1515/9783110365696
3. Krause U. Soziale Dynamiken mit vielen Interakteuren. Eine Problemskizze. In: Modellierung und Simulation von Dynamiken mit vielen interagierenden Akteuren, Universitat Bremen, 37–51 (1997).
4. Krause U. A discrete nonlinear and non-autonomous model of consensus formation. In: Communications in Difference Equations, 227–236. Amsterdam, Gordon and Breach (2000).
5. Hegselmann R., Krause U. Opinion dynamics and bounded confidence: Models, analysis and simulation. Journal of Artificial Societies and Social Simulation 5 (3) (2002).
6. Pilyugin S.Yu., Campi M.C. Opinion formation in voting processes under bounded confidence. Networks and Heterogeneous Media 14, 619–634 (2019). https://doi.org/10.3934/nhm.2019024
7. Bodunov N.A., Pilyugin S.Yu. Convergence to fixed points in one model of opinion dynamics. Journal of Dynamical and Control Systems (2020). https://doi.org/10.1007/s10883-020-09514-1
References
1. Ren W., Cao Y. Distributed Coordination of Multi-agent Networks. Emergent Problems, Models, and Issues. New York, Springer (2011).
2. Krause U. Positive Dynamical Systems in Discrete Time. Theory, Models, and Applications. In: De Gruyter Studies in Mathematics. Vol. 62. Berlin, De Gruyter (2015). https://doi.org/10.1515/9783110365696
3. Krause U. Soziale Dynamiken mit vielen Interakteuren. Eine Problemskizze. In: Modellierung und Simulation von Dynamiken mit vielen interagierenden Akteuren, Universitat Bremen, 37–51 (1997).
4. Krause U. A discrete nonlinear and non-autonomous model of consensus formation. In: Communications in Difference Equations, 227–236. Amsterdam, Gordon and Breach (2000).
5. Hegselmann R., Krause U. Opinion dynamics and bounded confidence: Models, analysis and simulation. Journal of Artificial Societies and Social Simulation 5 (3) (2002).
6. Pilyugin S.Yu., Campi M.C. Opinion formation in voting processes under bounded confidence. Networks and Heterogeneous Media 14, 619–634 (2019). https://doi.org/10.3934/nhm.2019024
7. Bodunov N.A., Pilyugin S.Yu. Convergence to fixed points in one model of opinion dynamics. Journal of Dynamical and Control Systems (2020). https://doi.org/10.1007/s10883-020-09514-1
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Published
2021-07-21
How to Cite
Pilyugin, S. Y., & Sabirova, D. Z. (2021). Dynamics of one continual sociological model. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8(2), 317–330. https://doi.org/10.21638/spbu01.2021.211
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Mathematics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
