A hunter-gatherer-farmer population model: new conditional symmetries and exact solutions with biological interpretation

TL;DR

This paper develops new conditional symmetries and exact solutions for a hunter-gatherer-farmer population model, enhancing understanding of its biological dynamics through advanced mathematical methods.

Contribution

It introduces novel Q-conditional symmetries and exact solutions for the model, extending the nonclassical method for PDE systems and providing biological insights.

Findings

New exact solutions with biological interpretation

Comparison with recent studies shows improved understanding

Enhanced mathematical framework for population modeling

Abstract

New Q-conditional (nonclassical) symmetries and exact solutions of the hunter-gatherer-farmer population model proposed by Aoki, Shida and Shigesada (Theor. Popul. Biol. 1996;50:1-17) are constructed. The main method used for the aforementioned purposes is an extension of the nonclassical method for system of partial differential equations. An analysis of properties of the exact solutions obtained and their biological interpretation are carried out. New results are compared with those derived in recent studies devoted to the same model.