Generalized solutions to bounded-confidence models

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