  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.
