A numerical algorithm for computing Neimark-Sacker bifurcation parameters

Author

Ueta, Tetsushi ; Chen, Guanrong ; Yoshinaga, Tsunehiro ; Kawakami, Hiroshi

Author_Institution

Fac. of Eng., Tokushima Univ., Japan

Volume

5

fYear

1999

fDate

1999

Firstpage

503

Abstract

We propose an efficient method for computing parameter values of the Neimark-Sacker bifurcation in this paper. To handle the complex eigenvalue problem, we expand the characteristic equation into a sum of determinants of the involving matrices. We solve for the location of the fixed point, period, parameter, and arguments of the complex eigenvalues for the bifurcation simultaneously, by using Newton´s method and solutions of variational equations. This algorithm does not rely on the analytic structure of the underlying system

Keywords

Newton method; bifurcation; chaos; eigenvalues and eigenfunctions; network parameters; nonlinear network analysis; variational techniques; Neimark-Sacker bifurcation parameters; Newton´s method; characteristic equation; complex eigenvalue problem; complex eigenvalues; determinants; fixed point; parameter values; variational equations; Bifurcation; Chaos; Coupling circuits; Differential equations; Eigenvalues and eigenfunctions; Limit-cycles; Newton method; Nonlinear circuits; Nonlinear equations; Tellurium;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 1999. ISCAS '99. Proceedings of the 1999 IEEE International Symposium on

Conference_Location

Orlando, FL

Print_ISBN

0-7803-5471-0

Type

conf

DOI

10.1109/ISCAS.1999.777619

Filename

777619