Chaotic attractor with a characteristic of torus

Torus doubling is known as one of the most interesting transition routes from a torus to chaos. In this paper, we investigate features of chaos observed after the end of a torus doubling which is generated in a four-dimensional (4-D) electrical circuit. It is clarified that this chaotic attractor remains strongly characteristic of a torus. This attractor is characterized by the Lyapunov exponents. The Poincare map of this attractor has one positive and one zero Lyapunov exponent. It behaves chaotically in the amplitude direction and behaves like a torus in the phase direction. The existence of a torus characteristic behind chaotic oscillation is well explained by an approximated one-dimensional (1-D) map obtained from the Poincare map.