1-D map for the double scroll family

Author

Chua, Leon O. ; Tichonicky, Irene

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., California Univ., Berkeley, CA, USA

Volume

38

Issue

3

fYear

1991

fDate

3/1/1991 12:00:00 AM

Firstpage

233

Lastpage

243

Abstract

The 1-D map π* (an approximation of the 2-D Poincare map) is used to study the periodic windows of the double scroll family. First, an algorithm based on the kneading theory is used to determine the structure and the order of appearance of periodic orbits in the 1-D map π*. This information is used to find the structure and the period of the corresponding orbits of the 3-D system. The results show that although the 1-D map π* is an approximation of the 2-D Poincare map, it gives much information about the periodic windows of the double scroll family. It is conjectured that the periodic orbits of the system are unknotted knots. Since they are equivalent to the trivial knot, it should be possible to obtain every periodic orbit from those of period-1 by making only an appropriate number of twists

Keywords

nonlinear network analysis; 2D Poincare map approximation; 3D system orbits; Chua´s circuit; double scroll family; kneading theory; periodic windows; strange attractor; Eigenvalues and eigenfunctions; Equations; Helium; Inductors; Linear circuits; Orbits; Periodic structures; Resistors; Supercapacitors; Vectors;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/31.101317

Filename

101317