Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria. (23rd March 2014)

• Record Type: Journal Article
• Authors: Geng, Fengjie; Zhao, Junfang
• Other Names: Han M. Academic Editor.; Jin Z. Academic Editor.; Xia Y. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2014(2014)
• Publication Date: 2014-03-23
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2014/585609
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : The bifurcations of heteroclinic loop with one nonhyperbolic equilibrium and one hyperbolic saddle are considered, where the nonhyperbolic equilibrium is supposed to undergo a transcritical bifurcation; moreover, the heteroclinic loop has an orbit flip and an inclination flip. When the nonhyperbolic equilibrium does not undergo a transcritical bifurcation, we establish the coexistence and noncoexistence of the periodic orbits and homoclinic orbits. While the nonhyperbolic equilibrium undergoes the transcritical bifurcation, we obtain the noncoexistence of the periodic orbits and homoclinic orbits and the existence of two or three heteroclinic orbits.