Geodesic
Bifurcations and Attractors in Bogdanov Map
In this paper, we study bifurcation space and the phase plane of the Bogdanov map. Specific bifurcation structures can be observed in parameter space, related for instance to embedded boxes structure and configurations of bifurcation curves of periodic points near the cusp. This model is a diffeomorphism. The dynamics is extremely rich, involving periodicity, quasi-periodicity and chaos. The method of the study is a numerical iteration to an attractor in which the guesses are inspired by the theory. Bifurcation diagrams obtained in different parameter planes are given and a sketch showing the cusp bifurcations, for the versal unfolding of Bogdanov map, is given. Phase plane is also studied, different attractors are shown, their evolution giving rise to chaotic attractors is explained. Basins of attraction are considered and fuzzy boundaries of basins are put in evidence. The study of such kind of diffeomorphisms can give an interesting contribution to nonlinear systems.
Classification : 28A80 
@article{VM_2004_6_4_a1,
     author = {Ilhem Djellit and Ibtissem Boukemara},
     title = {Bifurcations and {Attractors} in {Bogdanov} {Map}},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_2004_6_4_a1/}
}
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AU  - Ibtissem Boukemara
TI  - Bifurcations and Attractors in Bogdanov Map
JO  - Visual Mathematics
PY  - 2004
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IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VM_2004_6_4_a1/
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%0 Journal Article
%A Ilhem Djellit
%A Ibtissem Boukemara
%T Bifurcations and Attractors in Bogdanov Map
%J Visual Mathematics
%D 2004
%V 6
%N 4
%I mathdoc
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%G en
%F VM_2004_6_4_a1
Ilhem Djellit; Ibtissem Boukemara. Bifurcations and Attractors in Bogdanov Map. Visual Mathematics, Tome 6 (2004) no. 4. http://geodesic.mathdoc.fr/item/VM_2004_6_4_a1/