Effects of inhomogeneous influence of individuals on an order-disorder transition in opinion dynamics

Abstract

We study the effects of inhomogeneous influence of individuals on collective phenomena. We focus analytically on a typical model of the majority rule, applied to the completely connected agents. Two types of individuals $A$ and $B$ with different influence activity are introduced. The individuals $A$ and $B$ are distributed randomly with concentrations $\nu$ and $1-\nu$ at the beginning and fixed further on. Our main result is that the location of the order-disorder transition is affected due to the introduction of the inhomogeneous influence. This result highlights the importance of inhomogeneous influence between different types of individuals during the process of opinion updating.