Analysis of a class of Lotka--Volterra systems

A generalized two-dimensional cubic Lotka-Volterra model with infinitesimal parameters is studied. Three different cases have been considered, one non-degenerate and two degenerate. The local behavior of the model has been studied in the three cases. Six bifurcation diagrams with thirty different regions have been obtained in the non-degenerate case, respectively, sixteen diagrams with forty regions in the two degenerate cases.