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Discontinuities, generalized solutions and (dis)agreement in opinion dynamics

Francesca Ceragioli 1 Paolo Frasca 2
2 NECS - Networked Controlled Systems
GIPSA-DA - Département Automatique, Inria Grenoble - Rhône-Alpes
Abstract : This chapter is devoted to the mathematical analysis of some continuous-time dynamical systems defined by ordinary differential equations with discontinuous right-hand side, which arise as models of opinion dynamics in social networks. Discontinuities originate because of specific communication constraints, namely quantization or bounded confidence. Solutions of these systems may or may not converge to a state of agreement, where all components of the state space are equal. After presenting three models of interest, we elaborate on the properties of their solutions in terms of existence, completeness, and convergence.
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Francesca Ceragioli, Paolo Frasca. Discontinuities, generalized solutions and (dis)agreement in opinion dynamics. Sophie Tarbouriech, Antoine Girard, Laurentiu Hetel Control Subject to Computational and Communication Constraints, 475, Springer, pp.287-309, 2018, Lecture Notes in Control and Information Sciences, 978-3-319-78449-6. ⟨10.1007/978-3-319-78449-6_14⟩. ⟨hal-01739420⟩

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