Bifurcations of a Homoclinic Orbit to Saddle-Center in Reversible Systems. (4th November 2012)

• Record Type: Journal Article
• Authors: Qiao, Zhiqin; Xu, Yancong
• Other Names: Hao Xinan Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-11-04
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/678252
• Languages: English
• ISSNs: 1085-3375

Abstract

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.