Abstract : The "classical" PSO version is very simple but the user have to define some parameters (swarm size, neighbourhoods, some coefficients). An adaptive version like TRIBES [1, 2] does not have this drawback. It is also often more effective when the criterion takes into account only the relation "best value vs number of fitness evaluations". However it is more time consuming, for it performs some intermediate computations in order to take advantage of the information collected during the process. This can be quite annoying, or even unacceptabe for some (quasi) real time applications. That is why it is still interesting to just improve the classical version, without complicating it too much. The idea here is to mathematically analyse the behaviour of the particles when there is no improvement over several time steps. If the system is seen as a black box that displays only the best positions found so far by the particles, it happens nothing seen from outside, as there certainly happens something inside, which is worthly to study. Better parameters can be derived from such an analysis. Five of the suggested PSO variants are tested on five classical functions, just to bring out some that seems interesting.