Abstract and Applied Analysis
Volume 2013 (2013), Article ID 152518, 11 pages
http://dx.doi.org/10.1155/2013/152518
Research Article

The Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues

Xiaodong Li,1 Weipeng Zhang,1 Fengjie Geng,2 and Jicai Huang3

1School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China
2School of Information Engineering, China University of Geosciences (Beijing), Beijing 100083, China
3School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, China

Received 19 February 2013; Accepted 22 April 2013

Academic Editor: Maoan Han

Copyright © 2013 Xiaodong Li 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

The twisting bifurcations of double homoclinic loops with resonant eigenvalues are investigated in four-dimensional systems. The coexistence or noncoexistence of large 1-homoclinic orbit and large 1-periodic orbit near double homoclinic loops is given. The existence or nonexistence of saddle-node bifurcation surfaces is obtained. Finally, the complete bifurcation diagrams and bifurcation curves are also given under different cases. Moreover, the methods adopted in this paper can be extended to a higher dimensional system.