Asymptotic Expansion of the Heteroclinic Bifurcation for the Planar Normal Form of the 1:2 Resonance - Roberto, Luci A.F. [UNESP]; Da Silva, Paulo R. [UNESP]; Torregrosa, Joan (World Scientific Publishing, 2016)
We consider the family of planar differential systems depending on two real parameters x = y, y = δ1x + δ2y + x3 - x2y. 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 δ2 = c(δ1) = -1/5δ1 + O(δ1 2), δ1 < 0. We significantly improve the knowledge of this curve in a neighborhood of the origin.
Keywords: bifurcation diagram; Homoclinic connections; planar systems