Taming chaos: a numerical experiment using low-order LTI filters

Author

Hammad, Ayman A. ; Jonckheere, Edmond A.

Author_Institution

Dept. of Electr. Eng. Syst., Univ. of Southern California, Los Angeles, CA, USA

Volume

42

Issue

2

fYear

1995

fDate

2/1/1995 12:00:00 AM

Firstpage

111

Lastpage

115

Abstract

According to a recent paper by Jonckheere, Hammad, and Wu (1993), it is not possible to reduce the Kohnogorov-Sinai entropy by linear, stationary feedback, if the closed loop system is stable and minimum phase. This paper provides some extra insight into the understanding of this situation by bifurcation diagram (rather than entropy) analysis of three simple examples. In this numerical experiment, a chaotic signal is used as input to a linear filter that models the closed loop system. No forcing or tuning of the chaotic input is available. It appears that low-order LTI filters cannot tame chaos

Keywords

bifurcation; chaos; filters; linear network analysis; poles and zeros; Kohnogorov-Sinai entropy; bifurcation diagram; chaotic signal; closed loop system; linear time-invariant filters; low-order LTI filters; numerical experiment; Bifurcation; Chaos; Closed loop systems; Control systems; Entropy; Extraterrestrial measurements; Feedback loop; Helium; Logistics; Nonlinear filters;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.372851

Filename

372851