  We investigate, through a kinetic-exchange model, the impact that an external
field, like advertising and propaganda, has on opinion dynamics. We address the
situations where two opposite alternatives can be selected but the possibility
of indecision also exists. In this model, individuals influence each other
through pairwise interactions, which can be of agreement or disagreement, and
there are also external fields that can skew decision making. Two parameters
are used to model the interactions with the field: one measures the sensitivity
of the individuals to be influenced, another quantifies in which direction. We
study this model in a fully connected social network scenario, by means of
numerical simulations of the kinetic exchange dynamics and analytical results
derived from the mean-field rate equations. We show how the external bias gives
rise to imperfect bifurcations, and cusp catastrophes, allowing abrupt changes
and hysteresis depending on the level of disagreement in interpersonal
interactions and on the strength of the external influence.
