Systems without low-productive sources

Information Production Processes (IPPs) without low-productive sources are studied. A success-breeds-success or preferential attachment mechanism is established in which, from some point in time on, no new sources are created. Such systems are called mature systems. When time increases in mature systems the expected number of sources with a low number of items strictly decreases. An adaptation of the Naranan-Egghe model indicates that IPPs without low-productive sources must have small alpha exponents (α < 2) in their size-frequency power law descriptions. A positive reinforcement model explains all the essential properties. Using this approach it is shown that, when time increases in mature systems the alpha exponent of the power size-frequency function decreases, while, moreover, the minimum source size increases. Examples related to country and city sizes illustrate the concepts and results discussed in this article.