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.