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 attractorin a system of two coupled non-autonomous van der Pol oscillators (Kuznetsov,Phys. Rev. Lett., 95, 144101, 2005). At certain parameter values, in thefour-dimensional phase space of the Poincare map a toroidal domain (a directproduct of a circle and a three-dimensional ball) is determined, which ismapped into itself and contains the attractor we analyze. In accordance withthe computations, in this absorbing domain the conditions of hyperbolicity arevalid, which are formulated in terms of contracting and expanding cones in thetangent spaces (the vector spaces of the small state perturbations).