Nonlinear Opinion Dynamics With Tunable Sensitivity

We propose a continuous-time multi-option nonlinear generalization of linear weighted-average opinion dynamics. Nonlinearity is introduced saturating opinion exchanges, and this is enough to enable a significantly range of opinion-forming behaviors with our model as compared to linear and nonlinear models. For a group of agents that communicate over a network, these behaviors include multistable agreement and, tunable sensitivity to input, robustness to disturbance, flexible between patterns of opinions, and opinion cascades. We derive-dependent tuning rules to robustly control the system behavior and we state-feedback dynamics for the model parameters to make the behavior to changing external conditions. } The model provides new means for study of dynamics on natural and engineered networks, from spread and political polarization to collective decision making and task allocation.