On cyclicity of triangles and segments in quadratic systems
This paper deals with bifurcations, and limit cycles properties of a family of two-dimensional autonomous ordinary differential equations defined by two quadratic functions. A ``generator'' (or non perturbated) quadratic system, having three invariant lines (the two axes and an oblique line), is considered. It is perturbated by quadratic terms. Different situations of the generator system called ``bounded triangle'', ``unbounded triangle'', and the limit cases ``line at infinite case'' ``double invariant line case'', plus the Hamiltonian case, are studied. Other situations denoted ``bounded segments'', and ``unbounded segments'' are indicated. It is shown that after perturbation the maximal number of limit cycles is three for the bounded triangle case, and two for the unbounded triangle, one for the bounded segment.
scientific article; zbMATH DE number 810066