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

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

2012-01-31

arxiv.org/abs/1201.6657v1

Nonlinear Sciences

Chaotic Dynamics

7 pages, 7 figures, 1 table

Scientific paper

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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