A mathematical model of social group competition with application to the growth of religious non-affiliation

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.