Before revision:  Drawing inspiration from models in biology, physics, and social psychology, we apply a sigmoidal saturating function to inter-agent and intra-agent exchanges of opinions. The saturating function is the only nonlinearity in the model, yet we prove how it yields rapid and reliable formation of consensus, dissensus , and opinion cascades as a function of just a few parameters.
After revision:  Drawing inspiration from models in biology, physics, and social psychology, we apply a sigmoidal saturating function to inter-agent and intra-agent opinion exchanges. This yields simply parameterized dynamics that exhibit the range of opinion formation behaviors predicted by model-independent bifurcation theory but not exhibited by linear models or existing nonlinear models. Behaviors include rapid and reliable formation of consensus, dissensus , and opinion cascades as a function of just a few parameters.