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The modeling of opinion dynamics has seen much study in varying academicdisciplines. Understanding the complex ways information can be disseminated isa complicated problem for mathematicians as well as social scientists. Wepresent a nonlinear model of opinion dynamics that utilizes an environmentalaveraging protocol similar to the DeGroot and Freidkin-Johnsen models. Indeed,the way opinions evolve is complex and nonlinear effects ought to be consideredwhen modelling. For this model, the nonlinearity destroys the translationinvariance of the equations, as well as the convexity of the associated payoutfunctions. The standard theory for well-posedness and convergence no longerapplies and we must utilize the Brouwer topological degree and nonconvexanalysis in order to achieve these results. Numerical simulations of the modelreveal that the nonlinearity behaves similarly to the well-knownFriedkin-Johnsen for so-called "reasonable" opinions, but better models the wayagents that hold "extreme" opinions are more stubborn than their reasonablecounterparts.

Unique Nash equilibrium of a nonlinear model of opinion dynamics on networks with friction-inspired stubbornness