Bounded Confidence Model with Fixed Uncertainties and Extremists: The Opinions Can Keep Fluctuating Indefinitely

The bounded confidence model and its variants applied to moderate and extremist agents exhibit three types of attractors: central clusters, double extreme and single extreme clusters. These attractors are observed when the models include a dynamics on the uncertainties tending to decrease the moderate uncertainties when interacting with extremists. We show here that a new stationary state appears when the uncertainties are fixed, for large uncertainties of the moderates. In this stationary state, the opinions of moderate agents keep fluctuating without clustering, altogether forming a stable density which shape changes significantly when the parameters vary.