© 2016 World Scientific Publishing Company. 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(δ12), δ1 < 0. We significantly improve the knowledge of this curve in a neighborhood of the origin.
|Journal||International Journal of Bifurcation and Chaos|
|Publication status||Published - 1 Jan 2016|
- bifurcation diagram
- Homoclinic connections
- planar systems
Roberto, L. A. F., Da Silva, P. R., & Torregrosa, J. (2016). Asymptotic Expansion of the Heteroclinic Bifurcation for the Planar Normal Form of the 1:2 Resonance. International Journal of Bifurcation and Chaos, 26(1), . https://doi.org/10.1142/S0218127416500176