The productivity factor in the scientific community evolution

The mathematical model of productivity- and age-structured scientific community evolution is developed. This is the initial-boundary problem: for partial differential equation (of the Fokker–Planck type) about density function. The master equation describes the scientific community dynamics through the drift along the age component and the drift and diffusion with respect to productivity component. The boundary condition in integral form characterizes the birth of the new scientists by the skilled scientists with sufficient productivity level. The computation experiment implemented with the help of constructed approximate system permitted in particular to imitate the screening the less productive members of an age cohort during the time observed by the specialists in science of science. Some generalizations of the model and the empirical base developed for its practical realization are under discussion.