Generating upward sweeps in population using the Turchin--Korotayev model

TL;DR

This paper demonstrates how to induce upward population sweeps in the Turchin--Korotayev model by parameter modification, analyzes the system's stability, and identifies bifurcation points to understand population dynamics.

Contribution

It introduces a method to generate upward population trends through parameter changes and analyzes the model's stability and bifurcations, extending previous work on population cycles.

Findings

Upward population sweeps can be achieved by parameter adjustments.

The model has an unstable critical point.

Bifurcation points in parameter space are identified.

Abstract

The works of [Cha-DunAlvInoNieCarFieLaw,Cha-Dun] describe upward sweeps in populations of city-states and attempt to characterize such phenomenon. The model proposed in both [TurKor,Tur] describes how the population, state resources and internal conflict influence each other over time. We show that one can obtain an upward sweep in the population by altering particular parameters of the system of differential equations constituting the model given in [TurKor,Tur]. Moreover, we show that such a system has a unstable critical point and propose an approach for determining bifurcation points in the parameter space for the model.