Bifurcations and attractors in the Bogdanov map
by
Ilhem Djellit
University of Annaba, Dpt of Mathematics, BP 12-23000 Annaba-ALGERIA
Coauthors: Ibtissem Boukemara

Two-dimensional diffeomorphisms with quadratic terms arise in many applications. 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.The possibility to have two or more attractors in the phase plane can be also observed. In this paper, we study bifurcation space and the phase plane of  Bogdanov map. This model is a diffeomorphism. The dynamics is extremely rich, involving periodicity, quasiperiodicity 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 sketch showing the bifurcation curves for the versal unfolding of Bogdanov map of the cusp singularities 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.

Date received: September 23, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calu-10.