  When groups compete for members, the resulting dynamics of human social
activity may be understandable with simple mathematical models. Here, we apply
techniques from dynamical systems and perturbation theory to analyze a
theoretical framework for the growth and decline of competing social groups. We
present a new treatment of the competition for adherents between religious and
irreligious segments of modern secular societies and compile a new
international data set tracking the growth of religious non-affiliation. Data
suggest a particular case of our general growth law, leading to clear
predictions about possible future trends in society.
