Institut für Physik und Astronomie
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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.
Hyperbolic chaos of standing wave patterns generated parametrically by a modulated pump source
(2013)
We outline a possibility of hyperbolic chaotic dynamics associated with the expanding circle map for spatial phases of parametrically excited standing wave patterns. The model system is governed by a one-dimensional wave equation with nonlinear dissipation. The phenomenon arises due to the pump modulation providing the alternating excitation of modes with the ratio of characteristic scales 1 : 3. DOI: 10.1103/PhysRevE.87.040901