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Properties of the Dominant Behaviour of Quadratic Systems

Abstract We study the dominant terms of systems of Lotka-Volterra-type which arise in the the mathematical modelling of the evolution of many divers natural systems from the viewpoint of both symmetry and singularity analyses. The connections between an increase in the amount of symmetry possessed by the system and the possession of the Painlevé Property are noted. For specific values of the parameters of the system we see that possession of the Painlevé Property is characterised by a Left Painlevé Series rather than the more standard Right Painlevé Series.