Drawing and classifying phase portraits of planar polynomial vector fields

Abstract

Our aim is to study polynomial ordinary differential equations in two variables. To describe the behaviour of such systems it is important to have a tool which can visualize their phase portrait including the behaviour near infinity. For that purpose we developed a computer program called "Polynomial Planar Phase Portraits", which we abbreviate as P4. It permits to draw the phase portrait of a compactification on the Poincare disc or on a Poincare-Lyapunov disc. The program is an extension of previous work due to J. C. Artes and J. Llibre (see [Art90a, Art90b]). They developed a numeric program which can visualize the phase portraits of quadratic differential equations on the Poincare disc. The most essential information that we added deals with the study of the singularities and the change of the graphical interface.