Power Law Scaling for a System of Interacting Units with Complex Internal Structure

TL;DR

This paper introduces a model for systems of interacting units with complex internal structures, demonstrating its ability to predict empirical data over 20 years, highlighting power law scaling behaviors.

Contribution

The paper presents a novel mean field model for interacting units with multiplicative subunit growth and nonlinear interactions, validated against extensive empirical data.

Findings

Model accurately predicts empirical data over 20 years.

Power law scaling observed in system dynamics.

Nonlinear interactions among subunits are crucial for model accuracy.

Abstract

We study the dynamics of a system composed of interacting units each with a complex internal structure comprising many subunits. We consider the case in which each subunit grows in a multiplicative manner. We propose a model for such systems in which the interaction among the units is treated in a mean field approximation and the interaction among subunits is nonlinear. To test the model, we identify a large data base spanning 20 years, and find that the model correctly predicts a variety of empirical results.