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ISSN 2542-1905 (Online)

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Kuznetsov A. P., Sataev I. R. Verification of hyperbolicity conditions for a chaotic attractor in a system of coupled nonautonomous van der Pol oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 5, pp. 3-29. DOI: 10.18500/0869-6632-2006-14-5-3-29

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Verification of hyperbolicity conditions for a chaotic attractor in a system of coupled nonautonomous van der Pol oscillators

Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Sataev Igor Rustamovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

We present a method and results of numerical computations on verification of hyperbolic nature for the chaotic attractor in a system of two coupled nonautonomous van der Pol oscillators (Kuznetsov, Phys. Rev. Lett., 95, 2005, 144101). At selected parameter values, we indicate a toroidal domain in four-dimensional phase space of Poincare map (topologically, a direct product of a circle and a three-dimensional ball), which is mapped into itself and contains the attractor we analyze. In accordance with our computations, in this absorbing domain the conditions are valid guaranteeing hyperbolicity, which are formulated in terms of contracting and expanding cones in the vector spaces of the small state perturbations (the tangent spaces). We discuss also some numerical results illustrating certain attributes of hyperbolic dynamics.

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