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 μg and μd. 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 μg than μd which gives us an insight to the possible mechanisms affecting the popularity dynamics in a society.
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