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- Title
Homoclinic flip bifurcation with a nonhyperbolic equilibrium.
- Authors
Liu, Xingbo; Shi, Lina; Zhang, Dongmei
- Abstract
In this paper, the problem of homoclinic bifurcation accompanied by a transcritical bifurcation is investigated for high-dimensional systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. Under certain nongeneric conditions (orbit flip and inclination flip homoclinic orbits), the existence, nonexistence, coexistence and uniqueness of homoclinic and periodic orbits are studied. Some known results are extended.
- Subjects
BIFURCATION theory; ORBITAL mechanics; POINCARE maps (Mathematics); EQUILIBRIUM; ORBITS (Astronomy)
- Publication
Nonlinear Dynamics, 2012, Vol 69, Issue 1/2, p655
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-011-0294-x