| Issue |
Math. Model. Nat. Phenom.
Volume 8, Number 5, 2013
Bifurcations
|
|
|---|---|---|
| Page(s) | 71 - 83 | |
| DOI | https://doi.org/10.1051/mmnp/20138505 | |
| Published online | 17 September 2013 | |
On Global Bifurcations of Three-dimensional Diffeomorphisms Leading to Lorenz-like Attractors
1
Research Institute of Applied Mathematics and Cybernetics,
10, Ulyanova Str.,
603005
Nizhny Novgorod,
Russia
2
Imperial College, SW7 2AZ London, UK
⋆ Corresponding author. E-mail: Ivan.I.Ovsyannikov@gmail.com
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.
Mathematics Subject Classification: 37C05 / 37C29 / 37G25 / 37G35
Key words: homoclinic and heteroclinic orbits / bifurcations / strange attractors / saddle-focus
© EDP Sciences, 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.