Noise-based synchronization of bounded confidence opinion dynamics in heterogeneous time-varying communication networks
This paper studies noise-based synchronization of bounded confidence opinion dynamics in heterogeneous time-varying communication networks. The model is adapted from the Hegselmann \& Krause opinion dynamics with a time-varying undirected communication topology. The opinion of agent \(i\) at time \(t+1\) is updated as \(x_i(t+1)=1\) if \(x_i^*(t)>1\); \(x_i(t+1)=x_i^*(t)\) if \(0\le x_i^*(t)\le 1\); and \(x_i(t+1)=0\) if \(x_i^*(t)<0\). Here, \(x_i^*(t)\) is the average of the neighbors' states plus a random independent noise. The noise is assumed to be identically distributed for all agents and has a given finite bound. It is proved that the system is almost surely noise-synchronizable if and only if the graph is uniformly jointly connected. Numerical simulations have been performed over synthetic networks to validate the theoretical result.
scientific article; zbMATH DE number 7341955
scientific article