  This paper elaborates control strategies to prevent clustering effects in
opinion formation models. This is the exact opposite of numerous situations
encountered in the literature where, on the contrary, one seeks controls
promoting consensus. In order to promote declustering, instead of using the
classical variance that does not capture well the phenomenon of dispersion, we
introduce an entropy-type functional that is adapted to measuring pairwise
distances between agents. We then focus on a Hegselmann-Krause-type system and
design declustering sparse controls both in finite-dimensional and kinetic
models. We provide general conditions characterizing whether clustering can be
avoided as function of the initial data. Such results include the description
of black holes (where complete collapse to consensus is not avoidable), safety
zones (where the control can keep the system far from clustering), basins of
attraction (attractive zones around the clustering set) and collapse prevention
(when convergence to the clustering set can be avoided).
