Spatial Properties of a Mixed Linear-Nonlinear Model for Opinion Formation in Networks

A standard model for opinion formation in networks, which comprises a linear model for opinion-evolution coupled with a non-linear model for self-confidence dynamics, is considered. The main contribution of this study is to characterize the spatial pattern of the model dynamics in response to a local disruption. Specifically, we show that both the linear and nonlinear models exhibit a diffusive structure, such that responses to disruptions decay in amplitude along cutsets away from the disruption source in the network's graph. The spatial characterization is then used to motivate and develop a model reduction technique for the nonlinear self-confidence dynamics. Finally, the formal results and model reduction algorithm are illustrated in an example.