# Users' traffic on two-sided Internet platforms. Qualitative dynamics

## TL;DR

This paper introduces a dynamical system approach to model and analyze user traffic on two-sided Internet platforms, aiming to uncover underlying mechanisms and qualitative behaviors rather than just short-term predictions.

## Contribution

It presents a method to reconstruct differential equations from data, enabling qualitative analysis of platform user dynamics and external effects.

## Key findings

- Reconstructed governing differential equations from real platform data
- Analyzed phase portraits to understand platform dynamics
- Identified key characteristics of user interactions on platforms

## Abstract

Internet platforms' traffic defines important characteristics of platforms, such as pricing of services, advertisements, speed of operations. One can estimate the traffic with the traditional time series models like ARIMA, Holt-Winters, functional and kernel regressions. When using these methods, we usually smooth-out noise and various external effects in the data and obtain short-term predictions of processes. However, these models do not necessarily help us to understand the underlying mechanism and the tendencies of the processes. In this article, we discuss the dynamical system approach to the modeling, which is designed to discover the underlying mechanism and the qualitative properties of the system's phase portrait. We show how to reconstruct the governing differential equations from data. The external effects are modeled as system's parameters (initial conditions). Utilizing this new approach, we construct the models for the volume of users, interacting through Internet platforms, such as "Amazon.com", "Homes.mil" or "Wikipedia.org". Then, we perform qualitative analysis of the system's phase portrait and discuss the main characteristics of the platforms.