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

摘要

We present numerical verification of hyperbolic nature for chaotic attractor in a system of two coupled non-autonomous van der Pol oscillators [S.P. Kuznetsov, Phys. Rev. Lett. 95 (2005) 144101]. At certain parameter values, in the 4D phase space of the Poincaré map we indicate a toroidal domain (a direct product of a circle and a 3D ball), 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 vector spaces of the small state perturbations.