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EnglishSocial dynamics models may present discontinuities in the right-hand side of the dynamics for multiple reasons, including topology changes and quantization. Several concepts of generalized solutions for discontinuous equations are available in the literature and are useful to analyze these models. In this chapter, we study Caratheodory and Krasovsky generalized solutions for discontinuous models of opinion dynamics with state dependent interactions. We consider two definitions of “bounded confidence” interactions, which we respectively call metric and topological: in the former, individuals interact if their opinions are closer than a threshold; in the latter, individuals interact with a fixed number of nearest neighbors. We compare the dynamics produced by the two kinds of interactions in terms of existence, uniqueness and asymptotic behavior of different types of solutions.
Generalized solutions to opinion dynamics models with discontinuities / Ceragioli, Francesca; Frasca, Paolo; Piccoli, Benedetto; Rossi, Francesco. - STAMPA. - Crowd Dynamics Volume 3 - Modeling and Social Applications(2021).
| Titolo: | Generalized solutions to opinion dynamics models with discontinuities | |
| Autori: | ||
| Data di pubblicazione: | 2021 | |
| Titolo del libro: | Crowd Dynamics Volume 3 - Modeling and Social Applications | |
| Serie: | ||
| Abstract: | Social dynamics models may present discontinuities in the right-hand side of the dynamics for mul...tiple reasons, including topology changes and quantization. Several concepts of generalized solutions for discontinuous equations are available in the literature and are useful to analyze these models. In this chapter, we study Caratheodory and Krasovsky generalized solutions for discontinuous models of opinion dynamics with state dependent interactions. We consider two definitions of “bounded confidence” interactions, which we respectively call metric and topological: in the former, individuals interact if their opinions are closer than a threshold; in the latter, individuals interact with a fixed number of nearest neighbors. We compare the dynamics produced by the two kinds of interactions in terms of existence, uniqueness and asymptotic behavior of different types of solutions. | |
| Appare nelle tipologie: | 2.1 Contributo in volume (Capitolo o Saggio) |
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| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| Ceragioli_Frasca_Piccoli_Rossi_arxive.pdf | 1. Preprint / submitted version [pre- review] | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
http://hdl.handle.net/11583/2952352
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