Abstract and Applied Analysis
Volume 2012 (2012), Article ID 678252, 12 pages
http://dx.doi.org/10.1155/2012/678252
Research Article

Bifurcations of a Homoclinic Orbit to Saddle-Center in Reversible Systems

Zhiqin Qiao1 and Yancong Xu2

1Department of Mathematics, North University of China, Taiyuan 030051, China
2Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China

Received 24 July 2012; Accepted 13 October 2012

Academic Editor: Xinan Hao

Copyright © 2012 Zhiqin Qiao and Yancong Xu. 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 bifurcations near a primary homoclinic orbit to a saddle-center are investigated in a 4-dimensional reversible system. By establishing a new kind of local moving frame along the primary homoclinic orbit and using the Melnikov functions, the existence and nonexistence of 1-homoclinic orbit and 1-periodic orbit, including symmetric 1-homoclinic orbit and 1-periodic orbit, and their corresponding codimension 1 or codimension 3 surfaces, are obtained.