A strange attractor of the Smale-Williams type in the chaotic dynamics of a physical system
- Russian Academy of Sciences, Saratov Branch, Institute of Radio Engineering and Electronics (Russian Federation)
A nonautonomous nonlinear system is constructed and implemented as an experimental device. As represented by a 4D stroboscopic Poincare map, the system exhibits a Smale-Williams-type strange attractor. The system consists of two coupled van der Pol oscillators whose frequencies differ by a factor of two. The corresponding Hopf bifurcation parameters slowly vary as periodic functions of time in antiphase with one another; i.e., excitation is alternately transferred between the oscillators. The mechanisms underlying the system's chaotic dynamics and onset of chaos are qualitatively explained. A governing system of differential equations is formulated. The existence of a chaotic attractor is confirmed by numerical results. Hyperbolicity is verified numerically by performing a statistical analysis of the distribution of the angle between the stable and unstable subspaces of manifolds of the chaotic invariant set. Experimental results are in qualitative agreement with numerical predictions.
- OSTI ID:
- 21067731
- Journal Information:
- Journal of Experimental and Theoretical Physics, Vol. 102, Issue 2; Other Information: DOI: 10.1134/S1063776106020166; Copyright (c) 2006 Nauka/Interperiodica; Article Copyright (c) 2006 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7761
- Country of Publication:
- United States
- Language:
- English
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