Dual scaling properties of size and rank-frequency distributions in a model of alternating popularity growth and decay

Abstract

Here we propose a simple model of alternating exponential growths and decays, parametrized by the growth rate μg and decay rate μd, of the popularity of individuals quantified by daily mentions x in a newspaper. We report power-law distributions of yearly popularity p(s) and rank p(r) and observe simple trends for the values of the scaling exponents α and β, respectively, as a function of μ_g and μ_d. We show that a simple model of alternating growth and decay of name mentions results to stable power-law distributions for both p(s) and p(r). We also find that p(s) and p(r) are more influenced by μ_g than μ_d which gives us an insight to the possible mechanisms affecting the popularity dynamics in a society.