Title :
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
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;
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
DOI :
10.1109/ISCAS.1999.777619
