Hyperbolic attractor in a system of coupled non-autonomous van der Pol oscillators: Numerical test for expanding and contracting cones

Details Hyperbolic attractor in a system of coupled non-autonomous van der Pol oscillators: Numerical test for expanding and contracting cones Hyperbolic attractor in a system of coupled non-autonomous van der Pol oscillators: Numerical test for expanding and contracting cones

2006-09-04

arxiv.org/abs/nlin/0609004v1

Nonlinear Sciences

Chaotic Dynamics

14 pages, 7 figures

Scientific paper

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

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