Spiral orbits and oscillations in historical evolution of empires

TL;DR

This paper extends the asabiya theory of historical dynamics by introducing metaasabiya, resulting in a complex three-variable system that exhibits spirals and oscillations, modeling the rise and fall of empires.

Contribution

It introduces the concept of metaasabiya into the asabiya theory, creating a new dynamical system with unique features like spirals and oscillations in phase space.

Findings

The system exhibits spiraling orbits and oscillatory behavior.

Initial conditions determine series of rises and falls.

Features differ from traditional biological models.

Abstract

We introduce the concept of metaasabiya, the second non-material resource, to the asabiya theory of historical dynamics. We find that the resulting three variable dynamical system has peculiar features such as repelling or attracting axes and spiralling orbits in the phase space. Depending on the initial state, the system can go through series of oscillatory rises and falls, mimicking the geopolitical evolution of real-world polities. These distinctive features, absent in conventional Lotka-Volterra type biological systems, reveal the hidden richness inherent in the asabiya theory.