Relations between allometric scalings and fluctuations in complex systems: The case of Japanese firms

TL;DR

This study uncovers new allometric scaling relations and fluctuation patterns in Japanese firms, using large-scale data and probabilistic models to understand the underlying complex system dynamics.

Contribution

It introduces novel scaling relations including fluctuation distributions and develops probabilistic models linking scaling exponents to fluctuation magnitudes.

Findings

Discovered new scaling relations and fluctuation distributions.

Developed probabilistic models reproducing observed scaling behaviors.

Derived relations between scaling exponents and fluctuation magnitudes.

Abstract

To elucidate allometric scaling in complex systems, we investigated the underlying scaling relationships between typical three-scale indicators for approximately 500,000 Japanese firms; namely, annual sales, number of employees, and number of business partners. First, new scaling relations including the distributions of fluctuations were discovered by systematically analyzing conditional statistics. Second, we introduced simple probabilistic models that reproduce all these scaling relations, and we derived relations between scaling exponents and the magnitude of fluctuations.