Codimension 3 Non-resonant Bifurcations of Rough Heteroclinic Loops with One Orbit Flip*

• DOI: 10.1007/s11401-005-0472-6
• Publication Date: 2007-01-04T17:35:39Z
• Authors: Shuliang Shui; Deming Zhu
• Keywords: Heteroclinic orbit; Heteroclinic cycle; Heteroclinic bifurcation; Orbit (dynamics); Codimension; Homoclinic bifurcation

Heteroclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near a rough heteroclinic loop. This heteroclinic loop has a principal heteroclinic orbit and a non-principal heteroclinic orbit that takes orbit flip. The existence, nonexistence, coexistence and uniqueness of the 1-heteroclinic loop, 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold or three-fold 1-periodic orbit is also obtained.