Largest Lyapunov Exponents and Bifurcations of Stochastic Nonlinear Systems

Shock and Vibration

Volumn 3, Issue 4, 1996, Pages 313-320

  To, C W S ^a   Li, D M ^a  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012551718     PISSN: 10709622     EISSN: None     Source Type: Journal    
DOI: 10.3233/SAV-1996-3410     Document Type: Article

References (13)

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2. Arnold, L., Papanicolaou, G., and Wihstutz, V., 1986, “Asymptotic Analysis of the Lyapunov Exponent and Rotation Number of the Random Oscillator,” SIAM Journal of Applied Mathematics, Vol. 46, pp. 427–450.
3. Boxler, P., 1988, “Lyapunov Exponents and Stochastic Center Manifolds as Tools in Stability and Stochastic Bifurcation Theory,” Report No. 197, Institut für Dynamische Systeme, Universität Bremen, Bremen, Germany.
4. Boxler, P., 1989, “A Stochastic Version of Center Manifold Theory,” Journal of Probability Theoiy and Related Fields, Vol. 83, pp. 509–545.
5. Boxler, P., and Arnold, L., 1986, “Stochastische Bifurkationstheorie,” Report No. 163, Institut für Dynamische Systeme, Universität Bremen, Bremen, Germany.
6. Khas’minskii, R. Z., 1967, “Necessary and Sufficient Conditions for Asymptotic Stability of Linear Stochastic Systems,” Journal of Theory of Probability and Its Applications, Vol. 12, pp. 144–147.
7. Kozin, F., and Prodromou, S., 1971, “Necessary and Sufficient Conditions for Almost Sure Sample Stability of Linear Ito Equations,” SIAM Journal of Applied Mathematics, Vol. 21, pp. 413–424.
8. Pardoux, E., and Wihstutz, V., 1988, “Lyapunov Exponent and Rotation Number of Two-Dimensional Linear Stochastic Systems with Small Diffusion,” SIAM Journal of Applied Mathematics, Vol. 48, pp. 442–457.
9. Stratonovich, R. L., 1963, Topics in The Theory of Random Noise, Vol. 1, Gordon and Breach Science Publishers, New York.
10. To, C. W. S., 1993, “On Deterministic and Stochastic Center Manifolds,” in W. Z. Chien, Z. H. Guo and Y. Z. Guo, Proceedings of the Second International Conference on Nonlinear Mechanics, Beijing, Peking University Press, August 23-26, pp. 599–602.
11. To, C. W. S., and Li, D. M., 1991, “Degenerated Hopf Bifurcation in a Stochastically Disturbed System,” NDRLTR-9103, April 1991, Department of Mechanical Engineering, The University of Western Ontario.
12. To, C. W. S., and Li, D. M. and Huang, K. L., 1989, “Hopf Bifurcation in a Stochastically Disturbed System,” Engineering Science Preprints, ESP26.89003, 26th Annual Technical Meeting of the Society of Engineering Science, September 18-20, 1989, The University of Michigan, Ann Arbor, MI. (Also appeared as NDRL TR-9106, June 1991, Department of Mechanical Engineering, The University of Western Ontario.)
13. Wihstutz, V. (Ed.), 1986, Lyapunov Exponents, Lecture Notes in Mathematics, Vol. 1186, Springer-Verlag, New York.