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- Title
Nongeneric bifurcations near a nontransversal heterodimensional cycle.
- Authors
Liu, Xingbo; Wang, Xiaofei; Wang, Ting
- Abstract
In this paper bifurcations of heterodimensional cycles with highly degenerate conditions are studied in three dimensional vector fields, where a nontransversal intersection between the two-dimensional manifolds of the saddle equilibria occurs. By setting up local moving frame systems in some tubular neighborhood of unperturbed heterodimensional cycles, the authors construct a Poincaré return map under the nongeneric conditions and further obtain the bifurcation equations. By means of the bifurcation equations, the authors show that different bifurcation surfaces exhibit variety and complexity of the bifurcation of degenerate heterodimensional cycles. Moreover, an example is given to show the existence of a nontransversal heterodimensional cycle with one orbit flip in three dimensional system.
- Subjects
BIFURCATION theory; VECTOR fields; MANIFOLDS (Mathematics); NUMERICAL analysis; INTERPOLATION
- Publication
Chinese Annals of Mathematics, 2018, Vol 39, Issue 1, p111
- ISSN
0252-9599
- Publication type
Article
- DOI
10.1007/s11401-018-1055-7