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(x) over dot = y, (y) over dot = delta(1)x + delta(2)y + x(3) - x(2)y.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 delta(2) = c(delta(1)) = -1/5 delta(1) + O(delta(2)(1)), delta(1) < 0. We significantly improve the knowledge of this curve in a neighborhood of the origin.