Delay model for the dynamics of information units in the digital environment

Abstract: The digital revolution has transformed the exchange of information between people, blurring the traditional roles of sources and recipients. In this study, we explore the influence of this bidirectional feedback using a publicly available database of quotes, which act as distinct units of information flowing through the digital environment with minimal distortion. Our analysis highlights how the volume of these units decays with time and exhibits regular rebounds of varying intensities in media and blogs. To interpret these phenomena, we introduce a minimal model focused on delayed feedback between sources and recipients. This model not only successfully fits the variety of observed patterns but also elucidates the underlying dynamics of information exchange in the digital environment. Data fitting reveals that the mean attention to an information unit decays within approximately 13 hours in the media and within 2 hours in the blogs, with rebounds typically occurring between 1 and 4 days after the initial dissemination. Moreover, our model uncovers a functional relationship between the rate of information flow and the decay of public attention, suggesting a simplification in the mechanisms of information exchange in digital media. Although further research is required to generalize these findings fully, our results demonstrate that even a bare-bones model can capture the essential mechanisms of information dynamics in the digital environment.