In this talk, we will show different cubic polynomial systems in the plane, which simultaneously have limit cycles and invariant curves. Examples of Kolmogorov systems and Kukles systems are given. We show the existence of a cubic system having at least one limit cycle bounded by two invariant parabolas. For this system, we will also obtain the necessary conditions for the critical point in the interior of the bounded region to be a center.
Cubic System with Limit Cycles and Invariant Algebraic Curves
2019. 05. 02. 10:15