DocumentCode :
3161294
Title :
Effects of the Gear Discretization Order on the Computation of Bifurcation Boundaries
Author :
Bonet-Dalmau, J. ; Pala-Schonwalder, P. ; del Aguila-Lopez, Francisco ; Giralt-Mas, R.
Author_Institution :
Dept. of Signal Theor. & Commun., Tech. Univ. of Catalonia
fYear :
2006
fDate :
10-15 Sept. 2006
Firstpage :
466
Lastpage :
469
Abstract :
We extend a discrete-time approach for the analysis of the steady-state and local stability of nonlinear circuits, based on Gear discretizations, to compute the bifurcation boundaries of periodically forced nonlinear circuits. A bifurcation point may be detected by following a limit cycle solution as a function of a parameter until an eigenvalue crosses the unit circle. However, efficiency is improved by adding an extra equation that places this eigenvalue on the unit circle. This allows tracing directly the boundaries of distinct operation regions in a parameter space. As an application example, we study the fold, flip and Neimark-Sacker bifurcation boundaries of a forced van der Pol oscillator. While the effects of the discretization order on the computation of period-1 solutions are well-known, we investigate its effects on the accuracy of the bifurcation points and the associated period-p solutions. We conclude that there may be significant errors in computing bifurcation points and period-p solutions when the usual first and second order Gear discretizations are used
Keywords :
bifurcation; circuit stability; eigenvalues and eigenfunctions; nonlinear network analysis; relaxation oscillators; Gear discretization order; Neimark-Sacker bifurcation boundaries; bifurcation point; circuit stability; discrete-time approach; eigenvalue; forced van der Pol oscillator; limit cycle solution; local stability; periodically forced nonlinear circuits; steady-state stability; Bifurcation; Circuit analysis computing; Circuit stability; Eigenvalues and eigenfunctions; Gears; Limit-cycles; Nonlinear circuits; Nonlinear equations; Stability analysis; Steady-state; Bifurcation; circuit stability; nonlinear circuits;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Microwave Conference, 2006. 36th European
Conference_Location :
Manchester
Print_ISBN :
2-9600551-6-0
Type :
conf
DOI :
10.1109/EUMC.2006.281393
Filename :
4057851
Link To Document :
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