Chaotic attractor with a characteristic of torus

Author

Miyoshi, Tetsuya ; Nitanai, Takashi ; Inabe, N.

Author_Institution

Dept. of Inf. Sci., Utsunomiya Univ., Japan

Volume

47

Issue

6

fYear

2000

fDate

6/1/2000 12:00:00 AM

Firstpage

944

Lastpage

948

Abstract

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

Keywords

Lyapunov methods; bifurcation; chaos generators; circuit stability; hysteresis; nonlinear network analysis; piecewise linear techniques; 1D map; 4D electrical circuit; Lyapunov exponents; Poincare map; chaos; chaotic attractor; chaotic oscillation; four-dimensional electrical circuit; one-dimensional map; torus doubling; transition route; Chaos; Circuit analysis; Continuous time systems; Equations; Hysteresis; Information science; Nonlinear circuits; Nonlinear systems; Oscillators; Piecewise linear techniques;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.852951

Filename

852951