“Follow the leader” learning dynamics on networks

A learning dynamics on network is introduced, characterized by binary and multiple nonlinear interactions among the individuals distributed in the different nodes. A particular topology of the network is considered by introducing a leader node which influences all the other “follower” nodes without being influenced in turn. Numerical simulations are provided, particularly focusing on the effect of the network structure and of the nonlinear interactions on the emerging behaviour of the system. It turns out that the leader node always exhibits an autonomous evolution, while the follower nodes may have a regression when the interactions with the leader node are switched off. There is instead a remarkable change in the final configurations of the follower nodes, even if only one of them is connected to the leader: indeed, due to the microscopic interactions among them, all the follower nodes feel a strong “leader effect”.