Subharmonic oscillation modeling and MISO Volterra series

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 50, Issue 7, 2003, Pages 877-884

  Boaghe, Otilia M ^a   Billings, Stephen A ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Bifurcations; Chaos; Frequency response functions; Nonlinear oscillations; Response spectrum map; Subharmonics; Volterra series

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; CIRCUIT OSCILLATIONS; FOURIER TRANSFORMS; FREQUENCY RESPONSE; FUNCTIONS; HARMONIC GENERATION; MATHEMATICAL MODELS;

GENERALIZED FREQUENCY RESPONSE FUNCTIONS; SUBHARMONIC OSCILLATION; VOLTERRA SERIES;

NONLINEAR NETWORK ANALYSIS;

EID: 0041672387     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2003.813965     Document Type: Article

References (18)

1. S. A. Billings and O. M. Boaghe, "The response spectrum map, a frequency domain equivalent to the bifurcation diagram," Int. J. Bifurcation Chaos, vol. 11, no. 7, pp. 1961-1975, 2001.
2. S. A. Billings, S. Chen, and M. J. Korenberg, "Identification of MIMO nonlinear systems using a forward regressor orthogonal estimator," Int. J. Contr., vol. 49, no. 6, pp. 2157-2189, 1989.
3. S. Boyd, L. O. Chua, and C. A. Desoer, "Analytical foundations of Volterra series," IMA J. Math. Contr. Inform., vol. 1, pp. 243-282, 1984.
4. S. Boyd and L. O. Chua, "Fading memory and the problem of approximating nonlinear operators with Volterra series," IEEE Trans. Circuits Syst., vol. CAS-32, pp. 1150-1161, Nov. 1985.
5. L. O. Chua and C. Y. Ng, "Frequency domain analysis of nonlinear systems: formulation of transfer functions," Electron. Circuits Syst., vol. 3, no. 6, pp. 257-269, 1979.
6. M. J. Feigenbaum, "Universal behavior in nonlinear systems," Los Alamos Science, vol. 1, pp. 4-27, 1980.
7. D. A. George, "Continuous Nonlinear Systems," MIT Research Lab. of Electronics, Cambridge, MA, Tech. Rep. 355, 1959.
8. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields. New York: Springer-Verlag, 1983.
9. Y. Ishida, T. Yamamoto, and S. Murakami, "Nonstationary vibration of a rotating shaft with nonlinear spring characteristic during acceleration through a critical speed - (a critical speed of a 1/3-order subharmonic oscillation)," JSME Int. J. Ser. III, vol. 35, no. 3, pp. 360-368, 1992.
10. Y. Ishida, "Nonlinear vibrations and chaos in rotordynamics," JSME Int. J. Ser. C, vol. 37, no. 2, pp. 237-245, 1994.
11. S. Lefschetz, "Linear and nonlinear oscillations," in Modern Mathematics for the Engineer. New York: McGraw-Hill, 1956, pp. 7-30.
12. A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations. New York: Wiley, 1979.
13. J. C. Peyton-Jones and S. A. Billings, "Recursive algorithm for computing the frequency response of a class of nonlinear difference equation models," Int. J. Contr., vol. 50, no. 5, 1989.
14. S. S. Rao, Mechanical Vibrations. New York: Addison-Wesley, 1995.
15. I. W. Sandberg, "Nonlinear input-output maps and approximate representations," AT&T Tech. J., vol. 34, no. 8, pp. 1967-1983, 1985.
16. J. M. T. Thompson and H. B. Stewart, Nonlinear Dynamics and Chaos. New York: Wiley, 1991.
17. N. Wiener, Nonlinear Problems in Random Theory. New York: Wiley, 1958.
18. M. J. Feigenbaum, "Universal behavior in nonlinear systems," in Universality in Chaos, P. Predrag Cvitanovic, Ed. Bristol, U.K.: Adam Hilger, 1989, pp. 49-84.