On Global Bifurcations of Three-dimensional Diffeomorphisms Leading to Lorenz-like Attractors

We study dynamics and bifurcations of three-dimensional diffeomorphisms with nontransversal heteroclinic cycles. We show that bifurcations under consideration lead to the birth of Lorenz-like attractors. They can be viewed as attractors in the Poincare map for periodically perturbed classical Lorenz...

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Bibliographic Details
Published in:Mathematical modelling of natural phenomena 2013, Vol.8 (5), p.71-83
Main Authors: Gonchenko, S.V., Ovsyannikov, I.I.
Format: Article
Language:English
Subjects:
37C05
37C29
37G25
37G35
bifurcations
homoclinic and heteroclinic orbits
saddle-focus
strange attractors
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Summary:We study dynamics and bifurcations of three-dimensional diffeomorphisms with nontransversal heteroclinic cycles. We show that bifurcations under consideration lead to the birth of Lorenz-like attractors. They can be viewed as attractors in the Poincare map for periodically perturbed classical Lorenz attractors and hence they can allow for the existence of homoclinic tangencies and wild hyperbolic sets.
ISSN:0973-5348
1760-6101
DOI:10.1051/mmnp/20138505