Discontinuities, Generalized Solutions, and (Dis)agreement in Opinion Dynamics

Ceragioli, Francesca; Frasca, Paolo

doi:10.1007/978-3-319-78449-6_14

Cited by 6 publications

(3 citation statements)

References 49 publications

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“…The full proof of the result for (2) was given in [36], which extended partial results from [9,13,15]. Here we prove the corresponding claims for (3) in Section 3.…”

Section: Mathematical Models and Main Resultssupporting

confidence: 55%

See 1 more Smart Citation

Generalized solutions to opinion dynamics models with discontinuities

Ceragioli¹,

Frasca²,

Piccoli³

et al. 2021

Preprint

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Social 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.

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“…The full proof of the result for (2) was given in [36], which extended partial results from [9,13,15]. Here we prove the corresponding claims for (3) in Section 3.…”

Section: Mathematical Models and Main Resultssupporting

confidence: 55%

“…• Extending the scope of our analysis to include dynamical models with other types of discontinuities, as those generated by quantization [15] or hybrid setting [25].…”

Section: Future Directionsmentioning

confidence: 99%

Generalized solutions to opinion dynamics models with discontinuities

Ceragioli¹,

Frasca²,

Piccoli³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The neighborhoods depend on the current state and, therefore, on time. This fact makes dynamics (1) a piecewise-continuous system [11]. Its solutions shall be intended in a semi-classical sense, that is, as piecewise-smooth solutions φ(t) such that the right-derivative of the solution is equal to the righthand side at all times, that is, lim…”

Section: Mathematical Modelmentioning

confidence: 99%

Modeling limited attention in opinion dynamics by topological interactions

Ceragioli¹,

Frasca²,

Rossi³

2020

Preprint

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This work explores models of opinion dynamics with opiniondependent connectivity. Our starting point is that individuals have limited capabilities to engage in interactions with their peers. Motivated by this observation, we propose a continuous-time opinion dynamics model such that interactions take place with a limited number of peers: we refer to these interactions as topological, as opposed to metric interactions that are postulated in classical bounded-confidence models. We observe that topological interactions produce equilibria that are very robust to disruptions.

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