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A hunter-gatherer–farmer population model: Lie symmetries, exact solutions and their interpretation

Published online by Cambridge University Press:  27 February 2018

R. M. CHERNIHA  and
V. V. DAVYDOVYCH
R. M. CHERNIHA
Affiliation:
Institute of Mathematics, NAS of Ukraine, 3 Tereshchenkivs'ka Street, 01004 Kyiv, Ukraine emails: r.m.cherniha@gmail.com, davydovych@imath.kiev.ua
V. V. DAVYDOVYCH
Affiliation:
Institute of Mathematics, NAS of Ukraine, 3 Tereshchenkivs'ka Street, 01004 Kyiv, Ukraine emails: r.m.cherniha@gmail.com, davydovych@imath.kiev.ua
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Abstract

The Lie symmetry classification of the known three-component reaction–diffusion system modelling the spread of an initially localized population of farmers into a region occupied by hunter-gatherers is derived. The Lie symmetries obtained for reducing the system in question to systems of ordinary differential equations (ODEs) and constructing exact solutions are applied. Several exact solutions of travelling front type are also found, their properties are identified and biological interpretation is discussed.

Keywords

Reaction–diffusion systemdiffusive Lotka–Volterra systemLie symmetryexact solutiontravelling front
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Issue 2 , April 2019 , pp. 338 - 357
Copyright
Copyright © Cambridge University Press 2018 

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