Resonant Homoclinic Flips Bifurcation in Principal Eigendirections

Tiansi Zhang, Xiaoxin Huang and Deming Zhu

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
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https://doi.org/10.1155/2013/267826

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:267826

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