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

@article{citeulike:5290132, 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.}, author = {Bomze, Immanuel}, citeulike-article-id = {5290132}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/BF00318088}, citeulike-linkout-1 = {http://www.springerlink.com/content/pr554j1230151t71}, day = {7}, doi = {10.1007/BF00318088}, journal = {Biological Cybernetics}, keywords = {evolution, game\_theory, lotka\_volterra, replicator}, month = {October}, number = {3}, pages = {201--211}, posted-at = {2009-07-28 13:17:54}, priority = {2}, title = {Lotka-Volterra equation and replicator dynamics: A two-dimensional classification}, url = {http://dx.doi.org/10.1007/BF00318088}, volume = {48}, year = {1983} }

TY - JOUR ID - citeulike:5290132 L3 - citeulike-article-id:5290132 N2 - 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. IS - 3 JF - Biological Cybernetics EP - 211 TI - Lotka-Volterra equation and replicator dynamics: A two-dimensional classification VL - 48 SP - 201 KW - evolution KW - game_theory KW - lotka_volterra KW - replicator AU - Bomze, Immanuel PY - 1983/10/07/ UR - http://dx.doi.org/10.1007/BF00318088 ER -