Bifurcation sequences at 1:4 resonance: an inventory
- 1 May 1994
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 7 (3) , 1073-1091
- https://doi.org/10.1088/0951-7715/7/3/017
Abstract
The problem of 1:4 resonance of a closed orbit of a vector field in R3 leads to the study of the Z4-equivariant planar vector field, in complex notation, z=ei alpha z+Az mod z mod 2+z3 where A in C and alpha in R are parameters. The parameter A-plane is divided into at least 48 different regions with topologically different bifurcation sequences under variation of the parameter alpha . We present an inventory of computer generated pictures of the bifurcation sequences. In contrast to sketches, the pictures show the physical appearance of the system. For example, some limit cycles are square-shaped and some saddle-node bifurcations are cusp-like. The knowledge of these interesting features can stimulate further research. They are discussed along with the problems of the computation.Keywords
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