Generalized solutions to boundedconfidence models
Abstract
Boundedconfidence models in social dynamics describe multiagent systems, where each individual interacts only locally with others. Several models are written as systems of ordinary differential equations with discontinuous righthand side: this is a direct consequence of restricting interactions to a bounded region with nonvanishing strength at the boundary. Various works in the literature analyzed properties of solutions, such as barycenter invariance and clustering. On the other side, the problem of giving a precise definition of solution, from an analytical point of view, was often overlooked. However, a rich literature proposing different concepts of solution to discontinuous differential equations is available. Using several concepts of solution, we show how existence is granted under general assumptions, while uniqueness may fail even in dimension one, but holds for almost every initial conditions. Consequently, various properties of solutions depend on the used definition and initial conditions.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.00755
 arXiv:
 arXiv:2012.00755
 Bibcode:
 2020arXiv201200755P
 Keywords:

 Mathematics  Optimization and Control