Title :
Computations of limit cycles via higher-order harmonic balance approximation
Author :
Moiola, Jorge ; Chen, Guanrong
Author_Institution :
Departamento de Ing. Electrica, Univ. Nacional del Sur, Babia Blanca, Argentina
fDate :
5/1/1993 12:00:00 AM
Abstract :
The detection of limit cycles arising from Hopf bifurcation phenomena by applying the harmonic balance method with different higher-order approximations is discussed. The results are presented using a graphical procedure that indicates clearly how the predictions of amplitude and frequency of a periodic solution can be improved by using higher and higher order approximations. Complete and explicit formulas for eighth-order harmonic balance approximation are provided
Keywords :
bifurcation; limit cycles; stability; Hopf bifurcation phenomena; amplitude; frequency; higher-order harmonic balance approximation; limit cycles; periodic solution; Bifurcation; Differential equations; Eigenvalues and eigenfunctions; Feedback; Frequency; Jacobian matrices; Laplace equations; Limit-cycles; Steady-state; Vectors;
Journal_Title :
Automatic Control, IEEE Transactions on
