Lotka-Volterra equation and replicator dynamics: A two-dimensional classification
Copyright policy )Lotka-Volterra equation and replicator dynamics: A two-dimensional classification
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.
- University of Vienna Austria
- Universitätszahnklinik Wien Austria
classification of two-dimensional phase flows, replicator equation, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, 101004 Biomathematics, classification of phase portraits of generalized Lotka-Volterra equation, Stability of solutions to ordinary differential equations, game dynamics, Structural stability and analogous concepts of solutions to ordinary differential equations, 101004 Biomathematik, Problems related to evolution, Animal behavior
classification of two-dimensional phase flows, replicator equation, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, 101004 Biomathematics, classification of phase portraits of generalized Lotka-Volterra equation, Stability of solutions to ordinary differential equations, game dynamics, Structural stability and analogous concepts of solutions to ordinary differential equations, 101004 Biomathematik, Problems related to evolution, Animal behavior
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