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

作者：Roberto Luci A F^*; da Silva Paulo R^*; Torregrosa Joan^*

来源：International Journal of Bifurcation and Chaos, 2016, 26(1): 1650017.

DOI：10.1142/S0218127416500176

• Homoclinic connections
• planar systems
• bifurcation diagram

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.

• 出版日期2016-1
• 单位Univ Estadual Paulista