  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.
