VERIFICATION OF HYPERBOLICITY CONDITIONS FOR A CHAOTIC ATTRACTOR IN A SYSTEM OF COUPLED NONAUTONOMOUS VAN DER POL OSCILLATORS
Cite this article as:
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: https://doi.org/10.18500/0869-6632-2006-14-5-3-29
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 Poincar´ e 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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BibTeX
author = {A. P. Kuznetsov and I. R. Sataev},
title = {VERIFICATION OF HYPERBOLICITY CONDITIONS FOR A CHAOTIC ATTRACTOR IN A SYSTEM OF COUPLED NONAUTONOMOUS VAN DER POL OSCILLATORS},
year = {2006},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {14},number = {5},
url = {https://old-andjournal.sgu.ru/en/articles/verification-of-hyperbolicity-conditions-for-chaotic-attractor-in-system-of-coupled},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2006-14-5-3-29},pages = {3--29},issn = {0869-6632},
keywords = {-},
abstract = { 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 Poincar´ e 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. }}