A simple class of quadratic systems
The author, using ideas of \textit{A. L. Neto} [Invent. Math. 59, 67-76 (1980; Zbl 0448.34012)], shows that a plane quadratic system with only one finite critical point and one critical point at infinity, has at most one limit cycle. This generalizes and simplifies work of \textit{D. E. Koditschek} and \textit{K. S. Narendra} [J. Differ. Equations 54, 181-195 (1984; Zbl 0498.34018)], originating in control theory. Subsequently Boll, Gasull and Llibre [preprint, Barcelona] have determined all cases in which Neto's method may be applied. (They have also pointed out that the description of the phase portrait in the author's case (ii) requires modification.)
scientific article; zbMATH DE number 3973338
scientific article