A "saddle-node" bifurcation scenario for birth or destruction of a Smale-Williams solenoid
- Formation or destruction of hyperbolic chaotic attractor under parameter variation is considered with an example represented by Smale-Williams solenoid in stroboscopic Poincare map of two alternately excited non-autonomous van der Pol oscillators. The transition occupies a narrow but finite parameter interval and progresses in such way that periodic orbits constituting a "skeleton" of the attractor undergo saddle-node bifurcation events involving partner orbits from the attractor and from a non-attracting invariant set, which forms together with its stable manifold a basin boundary of the attractor.
Author details: | Olga B. Isaeva, Sergey P. Kuznetsov, Igor R. Sataev |
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DOI: | https://doi.org/10.1063/1.4766590 |
ISSN: | 1054-1500 |
Title of parent work (English): | Chaos : an interdisciplinary journal of nonlinear science |
Publisher: | American Institute of Physics |
Place of publishing: | Melville |
Publication type: | Article |
Language: | English |
Year of first publication: | 2012 |
Publication year: | 2012 |
Release date: | 2017/03/26 |
Volume: | 22 |
Issue: | 4 |
Number of pages: | 7 |
Funding institution: | RFBR [12-02-00342, 12-02-31342] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |