Bifurcation Phenomena of Opinion Dynamics in Complex Networks

In this paper, we study the opinion dynamics of Improved Deffuant model (IDM), where the convergence parameter mu is a function of the opposite's degree K according to the celebrity effect, in small-world network (SWN) and scale-free network (SFN). Generically, the system undergoes a phase transition from the plurality state to the polarization state and to the consensus state as the confidence parameter E increasing. Furthermore, the evolution of the steady opinion s(*). as a function of E, and the relation between the minority steady opinion s(*)(min) and the individual connectivity k also have been analyzed. Our present work shows the crucial role of the confidence parameter and the complex system topology in the opinion dynamics of IDM.