Math. Model. Nat. Phenom.
Volume 8, Number 5, 2013Bifurcations
|Page(s)||71 - 83|
|Published online||17 September 2013|
On Global Bifurcations of Three-dimensional Diffeomorphisms Leading to Lorenz-like Attractors
Research Institute of Applied Mathematics and Cybernetics,
10, Ulyanova Str.,
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
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