A Continuous Model for the Ecological Collapse of Easter Island

  • Bálint TakácsEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)


In this article a mathematical model describing the possible events that could have lead to the ecological catastrophe of Easter Island is extended in a way that instead of the originally spatially discrete model (the domain is split into several regions) now a spatially continuous one is considered (the number of each population is observed at each point of the domain). In other words, the original system of ordinary differential equations is transformed into a system of partial differential equations, and then the effect of the diffusion of the trees is observed, i.e. whether it stabilizes the system like in the original case, or not. It turned out that because the linearized system can be written in a pretty similar form to the matrix of the two dimensional case which was examined in a previous article [10], the same theorems can be said about this system, meaning that the increase of the diffusion of the trees actually stabilizes the system in this case too.


Differential equations Stability Easter Island Modeling Diffusion 



Supported by the ÚNKP-17-3 New National Excellence Program of the Ministry of Human Capacities.


  1. 1.
    Basener, W., Brooks, B., Radin, M., Wiandt, T.: Rat instigated human population collapse on Easter Island. Nonlinear Dyn. Psychol. Life Sci. 12(3), 227–240 (2008)Google Scholar
  2. 2.
    Basener, W., Brooks, B., Radin, M., Wiandt, T.: Spatial effects and turing instabilities in the invasive species model. Nonlinear Dyn. Psychol. Life Sci. 15(4), 455–464 (2011)MathSciNetGoogle Scholar
  3. 3.
    Hunt, T.: Rethinking the fall of Easter Island: new ecidence points to an alternative explanation for a civilization’s collapse. Am. Sci. 94, 412–419 (2006)CrossRefGoogle Scholar
  4. 4.
    Hunt, T.: Rethinking Easter Island’s ecological catastrophe. J. Archaeol. Sci. 34, 485–502 (2007)CrossRefGoogle Scholar
  5. 5.
    Hunt, T., Lipo, C.: The Statues Walked - What Really Happened on Easter Island. Accessed 2 Aug 2018
  6. 6.
    Perumpanani, A.J., Sherratt, J.A., Maini, P.K.: Phase differences in reaction-diffusion-advection systems and applications to morphogenesis. IMA J. Appl. Math. 55, 19–33 (1995)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Takács, B., Horváth, R., Faragó, I.: The effect of tree-diffusion in a mathematical model of Easter Island’s population. Electron. J. Qual. Theory Differ. Equ. 84, 1–11 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Takács, B.: Analysis of some characteristic parameters in an invasive species model. Annales. Univ. Sci. Budapest., Sect. Comp. 45, 119–133 (2016)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Takács, B.: Modeling the ecological collapse of Easter Island. Master’s thesis (2017).
  10. 10.
    Takács, B., Horváth, R., Faragó, I.: The effect of tree diffusion in a two dimensional continuous model for Easter Island. Eur. J. Math. (accepted)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Eötvös Loránd UniversityBudapestHungary

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