A nonlinear model of opinion dynamics on networks with friction-inspired stubbornness

Abstract

The modeling of opinion dynamics has seen much study in varying academic disciplines. Understanding the complex ways information can be disseminated is a complicated problem for mathematicians as well as social scientists. Inspired by the Cucker-Smale system of flocking dynamics, we present a nonlinear model of opinion dynamics that utilizes an environmental averaging protocol similar to the DeGroot and Freidkin-Johnsen models. Indeed, the way opinions evolve is complex and nonlinear effects ought to be considered when modelling. For this model, the nonlinearity destroys the translation invariance of the equations, as well as the convexity of the associated payout functions. The standard theory for well-posedness and convergence no longer applies and we must utilize the Brouwer topological degree and nonconvex analysis in order to achieve these results. Numerical simulations of the model reveal that the nonlinearity behaves similarly to the well-known Friedkin-Johnsen for so-called “reasonable” opinions, but better models the way agents that hold “extreme” opinions are more stubborn than their reasonable counterparts.

Please cite this paper as:

@article{reynolds2023nonlinear,
  title={A nonlinear model of opinion dynamics on networks with friction-inspired
 stubbornness},
  author={Reynolds, D. N. and Tudisco, F.},
  journal={arXiv:2304.07556},
  year={2023}
}

Keywords: Graphs networks opinion dynamics consensus compromise stubbornness flocking