Successive torus doubling

Author

Sekikawa, Munehisa ; Miyoshi, Tetsuya ; Inaba, Naohiko

Author_Institution

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

Volume

48

Issue

1

fYear

2001

fDate

1/1/2001 12:00:00 AM

Firstpage

28

Lastpage

34

Abstract

In this paper, we analyze circuits which exhibit a torus doubling route to chaos. Though some researchers insisted that torus doubling occurs a finite number of times, we show that the successive occurrence of a certain kind of torus doubling, which we call “swollen shape type bifurcation,” is observed in a certain region. This phenomenon has a very delicate structure, and when observed in a laboratory experiment is very interesting. In addition, a coupled system of a logistic map and a sin circle map is proposed as the simplest model which can explain the mechanism of the swollen shape type bifurcation. Also, the swollen shape type bifurcation is also observed in this system

Keywords

Lyapunov methods; bifurcation; chaos; coupled circuits; nonlinear network analysis; chaos; logistic map; sin circle map; successive occurrence; swollen shape type bifurcation; torus doubling route; Bifurcation; Chaos; Circuit analysis; Coupling circuits; Frequency; Laboratories; Logistics; Numerical analysis; Resonance; Shape;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.903185

Filename

903185