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2013 Resonant Homoclinic Flips Bifurcation in Principal Eigendirections
Tiansi Zhang, Xiaoxin Huang, Deming Zhu
Abstr. Appl. Anal. 2013: 1-7 (2013). DOI: 10.1155/2013/267826


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.


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Tiansi Zhang. Xiaoxin Huang. Deming Zhu. "Resonant Homoclinic Flips Bifurcation in Principal Eigendirections." Abstr. Appl. Anal. 2013 1 - 7, 2013.


Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1343.37038
MathSciNet: MR3143553
Digital Object Identifier: 10.1155/2013/267826

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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