A universal circuit for studying and generating chaos. I. Routes to chaos

Author

Chua, Leon O. ; Wu, Chai Wah ; Huang, Anshan ; Zhong, Guo-Qun

Author_Institution

Electron. Res. Lab., California Univ., Berkeley, CA, USA

Volume

40

Issue

10

fYear

1993

fDate

10/1/1993 12:00:00 AM

Firstpage

732

Lastpage

744

Abstract

In this introductory tutorial paper, we demonstrate the generality of Chua´s oscillator in generating chaos and bifurcation phenomena by electronic laboratory experiments which illustrate the standard routes to chaos, and by giving a result which shows that Chua´s oscillator can generate the same qualitative behavior as any member of a 21-parameter family C of continuous, odd-symmetric, piecewise-linear vector field in R³. This result is of fundamental importance because it unifies many previously published papers on chaotic circuits and systems under one umbrella, thereby obviating the need to analyze these circuits and systems as separate and unrelated systems. Indeed, every bifurcation and chaotic phenomena exhibited by any member of the family C is also exhibited by this universal circuit

Keywords

bifurcation; chaos; nonlinear network analysis; oscillators; piecewise-linear techniques; 21-parameter family C; Chua´s oscillator; bifurcation phenomena; chaos generation; piecewise-linear vector field; universal circuit; Bifurcation; Chaos; Circuits and systems; Diodes; Electric breakdown; Inductors; Oscillators; Piecewise linear techniques; Resistors; Vectors;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.246149

Filename

246149