The discrete-time Altafini model of opinion dynamics with communication delays and quantization

The discrete-time Altafini model is an opinion dynamics model in which the interactions among a group of agents are described by a time-varying signed digraph. This paper first uses graph theoretic constructions to study modified versions of the Altafini model in which there are communication delays or quantized communication. The condition under which consensus in absolute value or bipartite consensus is achieved proves to be the same as the condition in the delay-free case. The paper also analyzes the performance of the model where the information exchanged between neighboring agents is subject to a certain type of deterministic uniform quantization. We show that in finite time and depending on initial conditions, the model on any static, connected, undirected signed graph will either cause all agents to reach a quantized consensus in absolute value, or will lead all variables to oscillate in a small neighborhood around the absolute value.