Abstract and Applied Analysis (Jan 2013)

Resonant Homoclinic Flips Bifurcation in Principal Eigendirections

  • Tiansi Zhang,
  • Xiaoxin Huang,
  • Deming Zhu

DOI
https://doi.org/10.1155/2013/267826
Journal volume & issue
Vol. 2013

Abstract

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A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered. By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the Poincaré return map and the bifurcation equation. A detailed investigation produces the number and the existence of 1-homoclinic orbit, 1-periodic orbit, and double 1-periodic orbits. We also locate their bifurcation surfaces in certain regions.