Multi-agent systems with decaying confidence and commensurate time-delays

Abstract

In this paper we consider a class of discrete-time multi-agent systems modeling opinion dynamics with decaying confidence in presence of delay in the communication channels. Delays arise naturally in such dynamics and they must be taken into account in the analysis. In the model under consideration, the delay presence results in a certain heterogeneous time repartition of the influence of one agent on the collective behavior of the network. The decaying confidence leads to reconfigurations of the communication topology due to the vanishing of some interactions. The initial conditions and the dynamics of the confidence determine the organization of agents in different groups in which the agreement is reached. The main result states that the agents which agree are those which are persistently connected. Some simulations illustrates the delay influence on the network pattern.