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

Luci A.F. Roberto, Paulo R. Da Silva, Joan Torregrosa

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Abstract

© 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.
Original languageEnglish
Article number1650017
JournalInternational Journal of Bifurcation and Chaos
Volume26
Issue number1
DOIs
Publication statusPublished - 1 Jan 2016

Keywords

  • bifurcation diagram
  • Homoclinic connections
  • planar systems

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    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), [1650017]. https://doi.org/10.1142/S0218127416500176