Convergence analysis of asymmetric homogeneous Deffuant-Weisbuch model

In this paper, we consider the convergence property of asymmetric homogeneous Deffuant-Weisbuch (DW) model, which is described by discrete-time equations driven by endogenously changing topologies. We focus on the dynamics analysis for this model when the agent selection probability is distributed independently and uniformly on the set of all agents. Although the opinions updated by a local rule are time-varying, we prove that all the opinions of the agents will convergent almost surely for any initial states, which verifies the aggregation characteristics of the asymmetric stochastic opinion dynamics models.