  This paper considers a discrete-time opinion dynamics model in which each
individual's susceptibility to being influenced by others is dependent on her
current opinion. We assume that the social network has time-varying topology
and that the opinions are scalars on a continuous interval. We first propose a
general opinion dynamics model based on the DeGroot model, with a general
function to describe the functional dependence of each individual's
susceptibility on her own opinion, and show that this general model is
analogous to the Friedkin-Johnsen model, which assumes a constant
susceptibility for each individual. We then consider two specific functions in
which the individual's susceptibility depends on the \emph{polarity} of her
opinion, and provide motivating social examples. First, we consider stubborn
positives, who have reduced susceptibility if their opinions are at one end of
the interval and increased susceptibility if their opinions are at the opposite
end. A court jury is used as a motivating example. Second, we consider stubborn
neutrals, who have reduced susceptibility when their opinions are in the middle
of the spectrum, and our motivating examples are social networks discussing
established social norms or institutionalized behavior. For each specific
susceptibility model, we establish the initial and graph topology conditions in
which consensus is reached, and develop necessary and sufficient conditions on
the initial conditions for the final consensus value to be at either extreme of
the opinion interval. Simulations are provided to show the effects of the
susceptibility function when compared to the DeGroot model.
