A strange attractor of the Smale-Williams type in the chaotic dynamics of a physical system |
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Authors: | S P Kuznetsov E P Seleznev |
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Institution: | (1) Saratov Branch, Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Saratov, 410019, Russia |
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Abstract: | A nonautonomous nonlinear system is constructed and implemented as an experimental device. As represented by a 4D stroboscopic Poincaré 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. |
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