Achieving Consensus of Opinion Dynamics in Networks with Stubborn Individuals

Abstract

The focus of this paper is to achieve opinion consensus for the opinion dynamics model in the network with stubborn individuals. It has been shown in most of the existing works that the opinion dynamics model in the network with stubborn individuals usually could not achieve opinion consensus. In contrast with these results, by adding an integral term that describes the historical knowledge of the neighboring opinions, we propose a modified model of the existing Taylor's model. The primary feature of this modified model is that as long as the underlying graph is connected, opinion consensus can be realized in the network with stubborn individuals. we prove this opinion consensus by employing a Lyapunov function based method. Finally, we present an example to illustrate our main result.