Analisi asintotica di modelli multi-agenti con ritardo nell'accoppiamento, interazione non-universale e leadership

This thesis aims to investigate the asymptotic behavior of solutions to opinion formation and flocking models. In particular, we study the effects of time delays, which represent either the reaction time of agents or the time required for information to propagate between them. Even arbitrarily small delays can induce instability phenomena in the system’s dynamics, making the stability analysis of such models a crucial topic of study. We establish consensus results for both the Hegselmann–Krause opinion formation model and the Cucker–Smale flocking model, examining several distinct scenarios. Specifically, we consider cases involving non-universal interactions between agents and communication failure. Furthermore, we extend our analysis to settings that include leadership structures and investigate the associated control problems arising in these frameworks. In addition, we study a Kuramoto model with non-universal interactions and time-delay effects, for which we provide an exponential decay estimate toward synchronization.