Eulerian Opinion Dynamics with Bounded Confidence and Exogenous Input
  The formation of opinions in a large population is governed by endogenous (human interactions) and exogenous (media influence) factors. In the analysis of opinion evolution in a large population, decision making rules can be approximated with non-Bayesian "rule of thumb" methods. This paper focuses on an Eulerian bounded-confidence model of opinion dynamics with a potential time-varying input. First, we prove some properties of this system's dynamics with time-varying input. Second, we derive a simple sufficient condition for opinion consensus, and prove the convergence of the population's distribution with no input to a sum of Dirac Delta functions. Finally, we define an input's attraction range, and for a normally distributed input and uniformly distributed initial population, we conjecture that the length of attraction range is an increasing affine function of population's confidence bound and input's variance. 
Anahita Mirtabatabaei, Peng Jia, Francesco Bullo
math.DS