  We study models of a society composed of a mixture of conformist and
reasonable contrarian agents that at any instant hold one of two opinions.
Conformists tend to agree with the average opinion of their neighbors and
reasonable contrarians to disagree, but revert to a conformist behavior in the
presence of an overwhelming majority, in line with psychological experiments.
The model is studied in the mean field approximation and on small-world and
scale-free networks. In the mean field approximation, a large fraction of
conformists triggers a polarization of the opinions, a pitchfork bifurcation,
while a majority of reasonable contrarians leads to coherent oscillations, with
an alternation of period-doubling and pitchfork bifurcations up to chaos.
Similar scenarios are obtained by changing the fraction of long-range rewiring
and the parameter of scale-free networks related to the average connectivity.
