Bifurcations of limit cycles in periodically forced nonlinear systems: the harmonic balance approach

Author

Piccardi, Carlo

Author_Institution

Dipartimento di Elettronica e Inf., Politecnico di Milano, Italy

Volume

41

Issue

4

fYear

1994

fDate

4/1/1994 12:00:00 AM

Firstpage

315

Lastpage

320

Abstract

The harmonic balance approach is used to analyze tangent (saddle-node) and flip (period-doubling) bifurcations of limit cycles in periodically forced nonlinear dynamical systems. An algebraic system of equations, whose unknowns are the coefficients of a truncated Fourier series, is defined and the relationships between the bifurcations of the solutions of this algebraic system and the tangent and flip bifurcations of the limit cycles are pointed out. Some examples are presented to illustrate the method and its accuracy

Keywords

bifurcation; harmonics; limit cycles; nonlinear dynamical systems; series (mathematics); algebraic system; flip bifurcations; harmonic balance; limit cycles; nonlinear dynamical systems; period-doubling; periodically forced nonlinear systems; saddle-node; tangent bifurcations; truncated Fourier series; Bifurcation; Chaos; Differential equations; Fourier series; Harmonic analysis; Limit-cycles; Nonlinear dynamical systems; Nonlinear equations; Nonlinear systems; Performance analysis;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.285687

Filename

285687