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Lotka-Volterra equation and replicator dynamics: A two-dimensional classification

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Abstract

The replicator equation arises if one equips a certain game theoretical model for the evolution of behaviour in animal conflicts with dynamics. It serves to model many biological processes not only in sociobiology but also in population genetics, mathematical ecology and even in prebiotic evolution. After a short survey of these applications, a complete classification of the two-dimensional phase flows is presented. The methods are also used to obtain a classification of phase portraits of the well-known generalized Lotka-Volterra equation in the plane.

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  1. Institut für Statistik und Informatik, Universität Wien, Austria

    Immanuel M. Bomze

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  1. Immanuel M. Bomze
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Bomze, I.M. Lotka-Volterra equation and replicator dynamics: A two-dimensional classification. Biol. Cybern. 48, 201–211 (1983). https://doi.org/10.1007/BF00318088

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  • DOI: https://doi.org/10.1007/BF00318088

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