The classification on the global phase portraits of two-dimensional Lotka-Volterra system (Q957739)

The authors present a complete classification of all quadratic planar Lotka-Volterra systems. By a very detailed investigation, they find 143 topologically inequivalent global phase portraits for these systems, up to time reversal. First, all systems with nontrivial closed orbits are examined separately. Then, using rescaling and normal forms, they generally classify the inhomogeneous quadratic systems under discussion, thus obtaining classes with up to three real parameters. These classes are treated separately, while the remaining homogeneous systems had already been analyzed in the literature. The main tool of investigation is the Poincaré compactification. All the global phase portraits are shown in the Poincaré disc.