Spectral Analysis of Growth in Spatial Lotka-Volterra Models

K.A. Hawick (New Zealand)

Keywords

LotkaVolterra; partial differential equations; spectral anal ysis; phase transitions; ecological model.

Abstract

The Lotka-Volterra coupled system of equations describ ing relationships between predators and prey has been ap plied to a number of spatial biological and ecological mod els by several authors. The equations need to be time integrated for long times on a large system to fully appreci ate 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 sug gest emergent and phase transitional behaviour in the pa rameters of the spatial Lotka-Volterra model

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