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Abstract and Applied Analysis
Volume 2013, Article ID 267826, 7 pages
http://dx.doi.org/10.1155/2013/267826
Research Article

Resonant Homoclinic Flips Bifurcation in Principal Eigendirections

1College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
2Department of Mathematics, East China Normal University, Shanghai 200062, China

Received 12 September 2013; Accepted 19 November 2013

Academic Editor: Svatoslav Staněk

Copyright © 2013 Tiansi Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.