On the limit cycles bifurcating from an ellipse of a quadratic center
The problem under consideration is to determine the influence of invariant algebraic curves of planar polynomial differential systems bifurcation of limit cycles. It is shown that in the case of polynomial perturbations of such systems algebraic invariant curves can generate algebraic limit cycles. By using the inverse integrating factor the authors prove that a perturbation of any quadratic system with an invariant ellipse surrounding a center within the class of quadratic systems provides the existence at least one 1-parameter family of such systems having a limit cycle bifurcating from the ellipse.
scientific article; zbMATH DE number 6376351
scientific article