On the Application of the Describing Function Technique to the Bifurcation Analysis of Nonlinear Systems

IEEE Transactions on Circuits and Systems II: Express Briefs

Volumn 54, Issue 4, 2007, Pages 343-347

  Lanza, Valentina ^a   Bonnin, Michele ^a   Gilli, Marco ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Bifurcation; describing function; limit cycles; non linear systems

Indexed keywords

BIFURCATION (MATHEMATICS); DESCRIBING FUNCTIONS; MICROWAVE CIRCUITS; OSCILLATORS (ELECTRONIC);

FLOQUET MULTIPLIERS; LIMIT CYCLE; SPECTRAL TECHNIQUES;

NONLINEAR SYSTEMS;

EID: 34247360723     PISSN: 15497747     EISSN: 15583791     Source Type: Journal    
DOI: 10.1109/TCSII.2006.890406     Document Type: Article

References (14)

1. K. S. Kundert and A. Sangiovanni-Vincentelli, “Simulation of non-linear circuits in the frequency domain,” IEEE Trans. Comput.-Aided Des., vol. CAD-5, no. 4, pp. 521–535, Oct. 1986.
2. A. I. Mees, Dynamics of Feedback Systems. New York: Wiley, 1981.
3. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, 2nd ed. New York: Springer-Verlag, 1998.
4. J. Guckenheimer and B. Meloon, “Computing periodic orbits and their bifurcations with automatic differentiation,” SIAM J. Sci. Comput., vol. 22, no. 3, pp. 951–985, 2000.
5. C. Piccardi, “Bifurcations of limit cycles in periodically forced non-linear systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 41, no. 4, pp. 315–320, Apr. 1994.
6. C. Piccardi, “Harmonic balance analysis of codimension-2 bifurcations in periodic systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 43, no. 12, pp. 1015–1018, Dec. 1996.
7. V. Rizzoli and A. Neri, “State of the art and present trends in nonlinear microwave techniques,” IEEE Trans. Microw. Theory Tech., vol. 36, no. 2, pp. 343–365, Feb. 1988.
8. V. Rizzoli, A. Neri, and D. Masotti, “Local stability analysis of microwave oscillators based on Nyquist's theorem,” IEEE Microw. Guided Wave Lett., vol. 7, no. 10, pp. 341–343, Oct. 1998.
9. F. Bonani and M. Gilli, “Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic balance approach,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 546, no. 8, pp. 881–890, Aug. 1999.
10. R. Genesio and A. Tesi, “A harmonic balance approach for chaos prediction: Chua's circuit,” Int. J. Bifurc. Chaos, vol. 2, no. 1, pp. 61–79, 1992.
11. M. Basso, R. Genesio, and A. Tesi, “A frequency method for predicting limit cycle bifurcations,” Nonlinear Dyn., vol. 13, pp. 339–360, 1997.
12. G. Torrini, R. Genesio, and A. Tesi, “On the computation of characteristic multipliers for predicting limit cycle bifurcations,” Chaos, Solitons, Fractals, vol. 9, pp. 121–133, 1998.
13. M. Gilli, F. Corinto, and P. Checco, “Periodic oscillations and bifurcations in cellular nonlinear networks,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 5, pp. 948–962, May 2004.
14. M. Farkas, Periodic Motions. New York: Springer Verlag, 1994.