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

Published online by Cambridge University Press:  17 September 2013

S.V. Gonchenko  and
I.I. Ovsyannikov
S.V. Gonchenko
Affiliation:
Research Institute of Applied Mathematics and Cybernetics, 10, Ulyanova Str., 603005 Nizhny Novgorod, Russia
I.I. Ovsyannikov*
Affiliation:
Research Institute of Applied Mathematics and Cybernetics, 10, Ulyanova Str., 603005 Nizhny Novgorod, Russia Imperial College, SW7 2AZ London, UK
*
⋆ Corresponding author. E-mail: Ivan.I.Ovsyannikov@gmail.com
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Abstract

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.

Keywords

homoclinic and heteroclinic orbitsbifurcationsstrange attractorssaddle-focus
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 5: Bifurcations , 2013 , pp. 71 - 83
Copyright
© EDP Sciences, 2013

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