Opinion dynamics in discrete-time networks with trust-mistrust interactions

Abstract

We consider a general version of opinion dynamics in discrete-time multi-agent networks when interactions among agents are either cooperative (trust) or antagonistic (mistrust). In particular, we study cluster consensus problem wherein agents divide into disjoint sets with non-identical opinions. We present a distributed synchronous update rule to achieve cluster consensus over structurally balanced networks and extend it for asynchronous and time-varying systems. We show that structural balance network is a sufficient condition to achieve cluster consensus but not a necessary condition. We give sufficient conditions for the system stability and propose a control mechanism to achieve cluster consensus in structurally unbalanced networks.