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

@article{Bomze2004LotkaVolterraEA, title={Lotka-Volterra equation and replicator dynamics: A two-dimensional classification}, author={Immanuel M. Bomze}, journal={Biological Cybernetics}, year={2004}, volume={48}, pages={201-211} }

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… Expand

#### 141 Citations

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The population dynamics of two interacting species modeled by the Lotka-Volterra (LV) model with general parameters that can promote or suppress the other species is studied and the intrinsic speed parameters of each species play a decisive role in species populations and wave properties. Expand

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