Bilinear effect in complex systems

TL;DR

This paper identifies a bilinear effect in the lifetime distributions of social systems like Chinese dynasties, modeled through a 3-layer network, revealing a widespread pattern in social dynamics.

Contribution

It introduces the concept of the bilinear effect in social systems and provides a network model explaining this phenomenon, supported by empirical data.

Findings

Distribution of dynasties' lifetimes shows two intersecting linear segments.

The 3-layer network model reproduces the bilinear effect.

The bilinear effect is observed in multiple social systems.

Abstract

The distribution of the lifetime of Chinese dynasties (as well as that of the British Isles and Japan) in a linear Zipf plot is found to consist of two straight lines intersecting at a transition point. This two-section piecewise-linear distribution is different from the power law or the stretched exponent distribution, and is called the Bilinear Effect for short. With assumptions mimicking the organization of ancient Chinese regimes, a 3-layer network model is constructed. Numerical results of this model show the bilinear effect, providing a plausible explanation of the historical data. Bilinear effect in two other social systems is presented, indicating that such a piecewise-linear effect is widespread in social systems.