Convergence to consensus results for Hegselmann-Krause type models with attractive-lacking interaction

In this paper, we analyze a Hegselmann-Krause opinion formation model with attractive-lacking interaction. More precisely, we investigate the situation in which the agents involved in an opinion formation process interact among themselves but can eventually suspend the exchange of information among each other at some times. Under quite general assumptions, we prove the exponential convergence to consensus for the model in presence of possible lack of interaction. We are also able to extend the consensus estimate in the case of Hegselmann-Krause models with time delay effects.