Asymptotic Expansion of the Heteroclinic Bifurcation for the Planar Normal Form of the 1:2 Resonance.

We consider the family of planar differential systems depending on two real parameters This system corresponds to the normal form for the 1:2 resonance which exhibits a heteroclinic connection. The phase portrait of the system has a limit cycle which disappears in the heteroclinic connection for the parameter values on the curve We significantly improve the knowledge of this curve in a neighborhood of the origin. [ABSTRACT FROM AUTHOR]