Before revision:  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. We further show how the network opinion dynamics exhibit both robustness to disturbance and ultrasensitivity to inputs. We design feedback dynamics for system parameters that enable active tuning of implicit thresholds in opinion formation for sensitivity to inputs, robustness to changes in input, opinion cascades, and flexible transitions between consensus and dissensus .
After revision:  The saturating function is the only nonlinearity in the model, yet we prove how it yields rapid and reliable formation of consensus, dissensus , robustness to changes in input, opinion cascades, and flexible transitions between consensus and dissensus .