The effect of tree-diffusion in a mathematical model of Easter Island’s population

Bálint Takács, Róbert Horváth, I. Faragó

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A number of theories have been constructed to explain the ecological collapse of the Easter Island. Basener and his co-authors proposed a mathematical model in the form of a system of ordinary differential equations. This system describes the change of the number of people, rats and trees in some subregions of the island. The movement of the human and rat populations was described by some diffusion parameters. They showed that the increase of the diffusion parameters of people and rats makes the system unstable. In the present paper we introduce a diffusion parameter for the tree population and show that this parameter has a stabilizing effect. Thus, it behaves oppositely to the other two diffusion parameters from the stability point of view. The results are demonstrated with some numerical calculations of the stability region.

Original languageEnglish
Article number84
JournalElectronic Journal of Qualitative Theory of Differential Equations
Volume2016
DOIs
Publication statusPublished - 2016

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Mathematical Model
Mathematical models
Rats
Ordinary differential equations
Stability Region
System of Ordinary Differential Equations
Numerical Calculation
Unstable

Keywords

  • Differential equations
  • Population dynamics
  • Stability of equilibria

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

The effect of tree-diffusion in a mathematical model of Easter Island’s population. / Takács, Bálint; Horváth, Róbert; Faragó, I.

In: Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2016, 84, 2016.

Research output: Contribution to journalArticle

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