A codimension two bifurcation with a third order Picard-Fuchs equation

AbstractUsing a third order Picard-Fuchs equation we show that a certain two parameter family of planar vectorfields for parameter values in a certain cone has a unique limit cycle, which is born from a Hopf bifurcation and dies in a saddle connection. This removes a superfluous hypothesis in Theorem 3.2, Chapter 13 of S. N. Chow and J. K. Hale (“Methods of Bifurcation Theory,” Springer-Verlag, New York, 1982)