Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems
Copyright policy )Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems
Although planar quadratic differential systems and their applications have been studied in more than one thousand papers, we still have no complete understanding of these systems. In this paper we have two objectives. First we provide a brief bibliographical survey on the main results about quadratic systems. Here we do not consider the applications of these systems to many areas as in Physics, Chemist, Economics, Biology, … Second we characterize the new class of planar separable quadratic polynomial differential systems. For such class of systems we provide the normal forms which contain one parameter, and using the Poincaré compactification and the blow up technique, we prove that there exist 10 non-equivalent topological phase portraits in the Poincaré disc for the separable quadratic polynomial differential systems.
- Sichuan University China (People's Republic of)
- Autonomous University of Barcelona Spain
Quadratic system, Research exposition (monographs, survey articles) pertaining to ordinary differential equations, Poincaré compactification, General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordinary differential equations, Separable system, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, phase portrait, separable system, quadratic system, Phase portrait
Quadratic system, Research exposition (monographs, survey articles) pertaining to ordinary differential equations, Poincaré compactification, General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordinary differential equations, Separable system, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, phase portrait, separable system, quadratic system, Phase portrait
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