Synchronization of networks of oscillators with distributed delay coupling

This paper studies the stability of synchronized states in networks, where couplings between nodes are characterized by some distributed time delay, and develops a generalized master stability function approach. Using a generic example of Stuart-Landau oscillators, it is shown how the stability of synchronized solutions in networks with distributed delay coupling can be determined through a semi-analytic computation of Floquet exponents. The analysis of stability of fully synchronized and of cluster or splay states is illustrated for several practically important choices of delay distributions and network topologies

Output regulation problems in hybrid systems

This entry discusses some of the salient features of the output regulation problem for hybrid systems, especially in connection with the steady-state characterization. In order to better highlight such peculiarities, the discussion is mostly focused on the simplest class of linear time-invariant systems exhibiting such behaviors. In comparison with the usual regulation theory, the role played by the zero dynamics and by the presence of more inputs than outputs is particularly striking

A hybrid model for opinion formation

This paper presents a hybrid model for opinion formation in a large group of agents exposed to the persuasive action of a small number of strong opinion leaders. The model is defined by coupling a finite difference equation for the dynamics of leaders opinion with a continuous integro-differential equation for the dynamics of the others. Such a definition stems from the idea that the leaders are few and tend to retain original opinions, so that their dynamics occur on a longer time scale with respect to the one of the other agents. A general well-posedness result is established for the initial value problem linked to the model. The asymptotic behavior in time of the related solution is characterized for some general parameter settings, which mimic distinct social scenarios, where different emerging behaviors can be observed. Analytical results are illustrated and extended through numerical simulation