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

Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 475)

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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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Politecnico di TorinoTorinoItaly
  2. 2.Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, GIPSA- LabGrenobleFrance

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