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

Nonchaotic Models and Predictability of the Users' Volume Dynamics on Internet Platforms