  Internet platforms' traffic defines important characteristics of platforms,
such as price of services, advertisements, speed of operations. The traffic is
usually estimated with the help of the traditional time series models (ARIMA,
Holt-Winters, etc.), which are successful in short term extrapolations of
sufficiently denoised signals. We propose a dynamical system approach for the
modeling of the underlying process. The method allows to discuss the global
qualitative properties of the dynamics' phase portrait and long term
tendencies. The proposed models are nonchaotic, the long term prediction is
reliable, and it explains the fundamental properties and trend of various types
of digital platforms. Because of these properties, we call the flow of these
models the {\it trending flow}. Utilizing the new approach, we construct the
two-sided platform models for the volume of users, that can be applied to
Amazon.com, Homes.mil or Wikipedia.org. We consider a generalization of the
two-sided platforms' models to multi-sided platforms. If the equations' are
cooperative, the flow is trending, and it helps to understand the properties of
the platforms and reliably predicts the long term behavior. We show how to
reconstruct the governing differential equations from time series data. The
external effects are modeled as system's parameters (initial conditions).
