0
TECHNICAL PAPERS

Stochastic Stability of Coupled Oscillators in Resonance: A Perturbation Approach

[+] Author and Article Information
N. Sri Namachchivaya

Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

H. J. Van Roessel

Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

J. Appl. Mech 71(6), 759-768 (Jan 27, 2005) (10 pages) doi:10.1115/1.1795813 History: Received January 30, 2002; Revised March 18, 2004; Online January 27, 2005
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.

References

Namachchivaya,  N. Sri, and Van Roessel,  H. J., 1993, “Maximal Lyapunov Exponent and Rotation Numbers for Two Coupled Oscillators Driven by Real Noise,” J. Stat. Phys., 71(3/4), pp. 549–567.
Namachchivaya,  N. Sri, Van Roessel,  H. J., and Doyle,  M. M., 1996, “Moment Lyapunov Exponent for Two Coupled Oscillators Driven by Real Noise,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 56, pp. 1400–1423.
Namachchivaya,  N. Sri, and Van Roessel,  H. J., 2001, “Moment Lyapunov Exponent and Stochastic Stability of Two Coupled Oscillators Driven by Real Noise,” ASME J. Appl. Mech., 68, pp. 1400–1412.
Molc̆anov,  S. A., 1978, “The Structure of Eigenfunctions of One-Dimensional Unordered Structures,” Math. USSR, Izv., 12(1), pp. 69–101.
Arnold,  L., 1984, “A Formula Connecting Sample and Moment Stability of Linear Stochastic Systems,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 44(4), pp. 793–802.
Arnold, L., Oeljeklaus, E., and Pardoux, E., 1986, “Almost Sure and Moment Stability for Linear Ito⁁ Equations,” Lyapunov Exponents, Lecture Notes in Mathematics, Vol. 1186, Springer-Verlag, New York, pp. 129–159.
Arnold, L., Kliemann, W., and Oeljeklaus, E., 1986, “Lyapunov Exponents of Linear Stochastic Systems,” Lyapunov Exponents, Lecture Notes in Mathematics, Vol. 1186 Springer-Verlag, New York, pp. 85–125.
Namachchivaya, N. Sri, Ramakrishnan, N., Van Roessel, H. J., and Vedula, L., 2003, “Stochastic Stability of Two Coupled Oscillators in Resonance: Averaging Approach,” Nonlinear Stochastic Dynamics, N. Sri Namachchivaya and Y. K. Lin, (eds.), Solid Mechanics and Its Applications, Vol. 110, pp. 167–178, Kluwer Dordrecht.
Arnold,  L., Doyle,  M. M., and Namachchivaya,  N. Sri, 1997, “Small Noise Expansion of Moment Lyapunov Exponents for General Two Dimensional Systems,” Dyn. Stab. Syst., 12(3), pp. 187–211.
Khasminskii,  R. Z., and Moshchuk,  N., 1998, “Moment Lyapunov Exponent and Stability Index for Linear Conservative System With Small Random Perturbation,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 58(1), pp. 245–256.
Pardoux,  E., and Wihstutz,  V., 1988, “Lyapunov Exponent and Rotation Number of Two-Dimensional Linear Stochastic Systems With Small Diffusion,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 48(2), pp. 442–457.
Bolotin, V. V., 1964, The Dynamic Stability of Elastic Systems, Holden-Day, San Francisco.
Wedig, W. V., 1988, “Lyapunov Exponents of Stochastic Systems and Related Bifurcation Problems,” Stochastic Structural Dynamics: Progress in Theory and Applications, S. T. Ariaratnam, G. I. Schuëller, and I. Elishakoff, eds., Elsevier Applied Science, London, pp. 315–327.

Figures

Grahic Jump Location
Variation of moment Lyapunov exponent, g2(p) with p

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In