Analytical properties of a three-compartmental dynamical demographic model

TL;DR

This paper analyzes a three-compartment demographic model using dynamical systems theory, revealing integrals of motion and conditions under which the model simplifies to well-known population growth models.

Contribution

It provides analytical criteria for the dominance of Malthusian and Kremer dynamics and reduces the model to Gompertz and Thoularis-Wallace forms under specific parameters.

Findings

Existence of two integrals of motion enabling reduction to a single ODE.

Criteria for dominance of Malthusian and Kremer dynamics.

Reduction to Gompertz and Thoularis-Wallace models under certain parameters.

Abstract

The three-compartmental demographic model by Korotaeyv-Malkov-Khaltourina, connecting population size, economic surplus, and educational level, is considered from the point of view of dynamical systems theory. It is shown that there exist two integrals of motion, which enable the system to be reduced to one non-linear ordinary differential equation. The study of its structure provides analytical criteria for the dominance ranges of the dynamics of Malthus and Kremer. Additionally, the particular ranges of parameters enable the derived general ordinary differential equations to be reduced to the models of Gompertz and Thoularis-Wallace.