A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems
This work presents a survey dedicated to the algebraic and explicit non-algebraic limit cycles of polynomial differential systems in \(\mathbb{R}^2\) and of discontinuous piecewise differential systems formed by two linear differential systems separated by a straight line in \(\mathbb{R}^2\). For the polynomial differential systems the authors collect the most essential results related to the number and configurations of their algebraic limit cycles. Investigations of the algebraic and explicit non-algebraic limit cycles for the mentioned class of discontinuous piecewise differential systems is a new area of research. Therefore, only the first results derived in this area are mentioned in the presented survey. Additionally, the authors recall seven open problems devoted to these types of limit cycles.
scientific article; zbMATH DE number 7363312
scientific article