### 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 language | English |
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Article number | 84 |

Journal | Electronic Journal of Qualitative Theory of Differential Equations |

Volume | 2016 |

DOIs | |

Publication status | Published - 2016 |

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### 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.

Research output: Contribution to journal › Article

*Electronic Journal of Qualitative Theory of Differential Equations*, vol. 2016, 84. https://doi.org/10.14232/ejqtde.2016.1.84

}

TY - JOUR

T1 - The effect of tree-diffusion in a mathematical model of Easter Island’s population

AU - Takács, Bálint

AU - Horváth, Róbert

AU - Faragó, I.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Differential equations

KW - Population dynamics

KW - Stability of equilibria

UR - http://www.scopus.com/inward/record.url?scp=84987797052&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84987797052&partnerID=8YFLogxK

U2 - 10.14232/ejqtde.2016.1.84

DO - 10.14232/ejqtde.2016.1.84

M3 - Article

AN - SCOPUS:84987797052

VL - 2016

JO - Electronic Journal of Qualitative Theory of Differential Equations

JF - Electronic Journal of Qualitative Theory of Differential Equations

SN - 1417-3875

M1 - 84

ER -