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European Journal of Mathematics

, Volume 5, Issue 3, pp 845–857 | Cite as

The effect of tree diffusion in a two-dimensional continuous model for Easter Island

  • Bálint Takács
  • Róbert Horváth
  • István FaragóEmail author
Research Article

Abstract

We consider a two-dimensional continuous model that describes the ecology of Easter Island. We show that the increase of the parameter corresponding to the diffusion of trees on the island has a stabilizing effect on the system, potentially preventing the collapse of island’s ecology. Next we give analytic proofs for these statements, and conduct numerical experiments that confirm these results.

Keywords

Differential equations Stability Easter Island Modeling Diffusion Finite element method 

Mathematics Subject Classification

35Q92 35B35 35K57 65M60 91D10 92D40 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Applied Analysis and Computational MathematicsEötvös Loránd UniversityBudapestHungary
  2. 2.Department of AnalysisBudapest University of Technology and EconomicsBudapestHungary
  3. 3.MTA-ELTE NumNet Research GroupBudapestHungary

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