A model of phase-coupled delay equations for the dynamics of word usage

Abstract

Word use presents regular oscillations mounted over slowly varying trends. These oscillations have beenrecently interpreted in terms of fashion-like cycles of interest and saturation, and modelled using a logisticequation with distributed delay. Here we show that the communities of semantically related words are partiallysynchronized. To account for this, we model the words of each community using logistic equations connectedwith a Kuramoto coupling. In this way, we test the simple hypothesis that the change in the occurrenceof a word depends linearly on the occurrence of its semantic neighbours. We show that this simple modelreproduces the coherence observed in the experimental communities using a single global coupling acrossmultiple languages, regardless of the network topology. Our results build confidence on a universal model oflanguage usage based on the interaction between cognitive forces and the sociocultural context.