A Generalized Preferential Attachment Model for Complex Systems
  Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. We investigate how the distribution depends on the initial conditions and changes from a pure exponential form for zero influx of new classes to a power law with an exponential cutoff form when the influx of new classes is substantial. We apply the model to study the growth dynamics of pharmaceutical industry. 
Kazuko Yamasaki, Kaushik Matia, Dongfeng Fu, Sergey V. Buldyrev, Fabio   Pammolli, Massimo Riccaboni and H. Eugene Stanley