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TECHNICAL PAPERS

On the Normal Forms Associated with High Dimensional Systems

[+] Author and Article Information
Koncay Huseyin, Weiyi Zhang

Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario, N2L 3G1

J. Vib. Acoust 123(2), 157-169 (Sep 01, 2000) (13 pages) doi:10.1115/1.1349886 History: Received June 01, 1999; Revised September 01, 2000
Copyright © 2001 by ASME
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References

Hassard, B. D., Kazarinoff, N. D., and Wan, Y. H., 1980, Theory and Applications of the Hopf Bifurcation, Cambridge University Press, Cambridge.
Knobloch,  E., 1986, “Normal Form Coefficients For the Nonresonant Double Hopf Bifurcation,” Phys. Lett. A, 116, pp. 365–368.
Huseyin, K., 1986, Multiple Parameter Stability Theory and its Applications, Oxford University Press.
Yu,  P., and Huseyin,  K., 1989, “Invariant Tori Arising at a General Critical Point of Co-dimension Three,” Appl. Math. Model., 13, pp. 506–523.
Yu,  P., 1998, “Computation of Normal Forms via a Perturbation Technique,” J. Sound Vib., 211, pp. 19–38.
Wang,  S. S., and Huseyin,  K., 1995, “Resonance Analysis of Nonlinear Systems with Compound Critical Points,” Int. J. Syst. Sci., 26, pp. 543–553.
Chow, S. N., Li, C. Z., and Wang, D., 1994, Normal Forms and Bifurcation of Planar Vector Fields, Cambridge University Press, Cambridge.
Chow,  S. N., Drachman,  B., and Wang,  D., 1990, “Computation of Normal Forms,” J. Comput. Appl. Math., 29, pp. 129–143.
Leung,  A. Y. T., and Zhang,  Q. S., 1998, “Higher-order Normal Form and Period Averaging,” J. Sound Vib., 217, pp. 795–806.
Zhang,  W. Y., Huseyin,  K., and Ye,  M., 2000, “On the Computation of the Coefficients Associated with High Order Normal Forms,” J. Sound Vib., 232, pp. 525–540.
Huseyin,  K., and Lin,  R., 1991, “An Intrinsic Multiple-Scale Harmonic Balance Method for Non-linear Vibration and Bifurcation Problems,” Int. J. Nonlinear Mech., 26, pp. 727–740.
Huseyin,  K., and Lin,  R., 1992, “A Perturbation Method for the Analysis of Vibrations and Bifurcations Associated with Non-autonomous Systems, Part I: Non-resonance Case,” Int. J. Nonlinear Mech., 27, pp. 203–217.
Zhang,  W. Y., Huseyin,  K., and Chen,  Y. S., 1998, “A New Approach for Obtaining Normal Forms of Nonlinear Systems,” J. Sound Vib., 210, pp. 609–625.
Zhang,  W. Y., Huseyin,  K., and Chen,  Y. S., 1998, “On the Analysis of Certain High Dimensional Systems with Inner Resonances,” J. Sound Vib., 213, pp. 739–756.
Mandadi,  V., and Huseyin,  K., 1980, “Nonlinear Bifurcation Analysis of Non-Gradient Systems,” Int. J. Nonlinear Mech., 15, pp. 159–172.
Zhang,  W. Y., and Huseyin,  K., 2000, “On the Relation Between the Methods of Averaging and Normal Forms,” Appl. Math. Model., 24, pp. 279–295.
Zhang,  W. Y., and Huseyin,  K., 2000, “An Algebraic Approach for Obtaining Nilpotent Normal Forms in Dimension 4,” IMA J. Appl. Math., 64, pp. 109–123.

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