Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues. (16th April 2014)

• Record Type: Journal Article
• Authors: Jin, Yinlai; Zhu, Xiaowei; Guo, Zheng; Xu, Han; Zhang, Liqun; Ding, Benyan
• Other Names: Han M. Academic Editor.; Jin Z. Academic Editor.; Xia Y. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2014(2014)
• Publication Date: 2014-04-16
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2014/716082
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits to establish the local coordinate systems in the small tubular neighborhoods of the heteroclinic orbits, we study the bifurcation problems of nontwisted heteroclinic loop with resonant eigenvalues. The existence, numbers, and existence regions of 1-heteroclinic loop, 1-homoclinic loop, 1-periodic orbit, 2-fold 1-periodic orbit, and two 1-periodic orbits are obtained. Meanwhile, we give the corresponding bifurcation surfaces.