||In this talk, first we describe a model of the posting behavior in Social Networks in topics which have negative externalities, and the second objective of it is to provide a content active filtering control such that the content diversity increase. By negative externalities, we mean that when the quantity of posted contents about some topic increases the popularity of posted contents decreases. We introduce a dynamical model to describe the posting behavior of users taking into account these externalities. Our model is based on stochastic approximations and sufficient conditions are provided to ensure its convergence to a unique rest point. We provide a close form of this rest point. Content Active Filtering (CAF) are actions taken by the administrator of the Social Network in order to promote some objectives related to the quantity of contents posted in various topics. As objective of the CAF we shall consider maximizing the diversity of posted contents.