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arXiv · 1201.6657

A "saddle-node" bifurcation scenario for birth or destruction of a Smale-Williams solenoid

Olga B. Isaeva·Sergey P. Kuznetsov·Igor R. Sataev
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Abstract

Formation or destruction of hyperbolic chaotic attractor under parameter variation is considered with an example represented by Smale--Williams solenoid in stroboscopic Poincar\'{e} 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.

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Olga B. Isaeva, Sergey P. Kuznetsov, Igor R. Sataev. 2012-01-31. A "saddle-node" bifurcation scenario for birth or destruction of a Smale-Williams solenoid. https://doi.org/10.1063/1.4766590

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