Computational Science Technical Note CSTN-092

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Spectral Analysis of Growth in Spatial Lotka-Volterra Models

K. A. Hawick

Archived May 2009, Revised March 2010

Abstract

The Lotka-Volterra coupled system of equations describing relationships between predators and prey has been applied to a number of spatial biological and ecological models by several authors. The equations need to be time-integrated for long times on a large system to fully appreciate the complex bulk behaviour that ensues spatially. This paper applies some spectral analysis methods to spatial Lotka-Volterra models to study length scales and phased-locked spatial wave patterns at early and long time scales. We employ a custom simulation code that supports near-interactive time study of model systems of around 100,000 spatial cells, and that are time-integrated stably for up to 10,000 iterations. We report on spectral image analysis and numerical scattering experimental techniques. These suggest emergent and phase transitional behaviour in the parameters of the spatial Lotka-Volterra model.

Keywords: Lotka-Volterra; partial differential equations; spectral analysis; phase transitions; ecological model.

Full Document Text: PDF version.

Citation Information: BiBTeX database for CSTN Notes.

BiBTeX reference:

@INPROCEEDINGS{CSTN-092,
  author = {K. A. Hawick},
  title = {Spectral Analysis of Growth in Spatial Lotka-Volterra Models},
  booktitle = {Proc. International Conference on Modelling and Simulation},
  year = {2010},
  number = {685-030},
  pages = {14-20},
  address = {Gabarone, Botswana},
  month = {6-8 September},
  publisher = {IASTED},
  institution = {Computer Science, Massey University},
  timestamp = {2009.09.06}
}


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