Confirmation of the Afraimovich-Shilnikov torus-breakdown theorem via a torus circuit

Author

Anishchenko, V.S. ; Safonova, M.A. ; Chua, Leon O.

Author_Institution

Dept. of Phys., Saratov State Univ., Russia

Volume

40

Issue

11

fYear

1993

fDate

11/1/1993 12:00:00 AM

Firstpage

792

Lastpage

800

Abstract

The Afraimovich-Shilnikov theorem on 2D torus breakdown is formulated and used to carry out a detailed numerical investigation of the bifurcation routes from the torus to chaos in a third-order torus circuit. Three scenarios of transition to chaos due to torus breakdown take place in this circuit in complete agreement with the theorem: 1) period-doubling bifurcations of the phase-locked limit cycles; 2) saddle-node bifurcation in the presence of a homoclinic structure; and 3) soft transition due to the loss of torus smoothness

Keywords

bifurcation; chaos; limit cycles; nonlinear network analysis; 2D torus breakdown; Afraimovich-Shilnikov torus-breakdown theorem; bifurcation routes; homoclinic structure; nonlinear networks; period-doubling bifurcations; phase-locked limit cycles; saddle-node bifurcation; soft transition; third-order torus circuit; torus circuit; torus smoothness; Bifurcation; Chaos; Circuits; Computer simulation; Electric breakdown; Equations; Helium; Limit-cycles; Physics; 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

10.1109/81.251815

Filename

251815