Resumen de A Complement to the Uniqueness of the Limit Cycle of a Family of Systems with Homogeneous Components
Consider the number of limit cycles of a family of systems with homogeneous components: x˙ = y, y˙ = −x3 +αx2 y + y3. We show that there is an α∗ < 0 such that the system has exactly one limit cycle for α ∈ (α∗, 0), while no limit cycle for the else region. This completes a previous result and also gives a positive answer to the second part of Gasull’s 3rd problem listed in the paper (SeMA J 78(3):233–269, 2021). To obtain this result, we mainly analyse the behavior of the heteroclinic separatrices at infinity.
