Hopf bifurcation for maps: a frequency-domain approach

Author

D´Amico, M.B. ; Moiola, Jorge L. ; Paolini, Eduardo E.

Author_Institution

Departamento de Ingenieria Electrica, Univ. Nacional del Sur, Bahia Blanca, Argentina

Volume

49

Issue

3

fYear

2002

fDate

3/1/2002 12:00:00 AM

Firstpage

281

Lastpage

288

Abstract

The application of the graphical Hopf theorem (GHT) as a tool for detecting invariant cycles in maps is presented. The invariant cycle emerging from the bifurcation is approximated using an analogous version of the GHT for continuous-time systems. This technique is formulated in the so-called frequency domain and it involves the use of the Nyquist stability criterion and the harmonic balance method. Some examples are included for illustration

Keywords

Nyquist stability; bifurcation; chaos; discrete time systems; frequency-domain analysis; harmonic analysis; invariance; GHT; Hopf bifurcation; Nyquist stability criterion; bifurcation; continuous-time systems; discrete-time systems; frequency domain; frequency-domain approach; graphical Hopf theorem; harmonic analysis; harmonic balance method; map invariant cycle detection; maps; Bifurcation; Circuits; Frequency domain analysis; Harmonic analysis; Helium; Heterojunction bipolar transistors; Instruments; MIMO; Nonlinear dynamical systems; Stability criteria;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.989161

Filename

989161