Modelling Ethnogenesis

TL;DR

This paper introduces a mathematical model of ethnogenesis using differential equations, capturing the rise and fall of civilizations through nonlinear dynamics, and explores interactions between multiple polities with both deterministic and stochastic approaches.

Contribution

It presents a novel differential equation model of ethnogenesis inspired by biological excitation phenomena, including interaction dynamics and stochastic effects.

Findings

Model successfully captures civilizational rise and fall dynamics.

Analytical and numerical methods validate the model's behavior.

Interaction effects between polities are characterized.

Abstract

Following the ideas of L.N.Gumilev, we introduce the mathematical model of ethnogenesis which describes the dynamics of subgroups in the developing polity in terms of ordinary differential equations. The bust dynamics associated with the rise and fall of civilisations is modelled as an excitation process, which is the non-linear phenomenon, well known in mathematical biology. We consider deterministic as well as the stochastic version of the model. We also expand the model to study the interaction between two polities undergoing ethnogenesis. Investigation is performed using analytical methods as well as numerical integration (i.e. MATLAB simulation).