Shifting Consensus in a Biased Compromise Model

We investigate the effect of bias on the formation and dynamics of opinion clusters in the bounded confidence model. For weak bias, we quantify the change in average opinion and potential dispersion and decrease in cluster size. For nonlinear bias modeling self-incitement, we establish coherent drifting motion of clusters on a background of uniform opinion distribution for biases below a critical threshold where clusters dissolve. Technically, we use geometric singular perturbation theory to derive drift speeds, we rely on a nonlocal center manifold analysis to construct drifting clusters near threshold, and we implement numerical continuation in a forward-backward delay equation to connect asymptotic regimes.