Stochastic Hopf bifurcation of quasi-nonintegrable-Hamiltonian systems

International Journal of Non-Linear Mechanics

Volumn 34, Issue 3, 1999, Pages 437-447

  Zhu, W Q ^a   Huang, Z L ^a  

^a ZHEJIANG UNIVERSITY   (China)

Author keywords

Quasi integrable Hamiltonian system; Stochastic averaging; Stochastic Hopf bifurcation; Stochastic stability

Indexed keywords

EID: 0001329762     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(98)00026-2     Document Type: Article

References (11)

1. C. Meunier, A.D. Verga, Noise and bifurcations, J. Statist. Phys. 50(1/2) (1988) 345-375.
2. N. Sri Namachchivaya, Stochastic bifurcation, Appl. Math. Comput. 38 (1990) 101-159
3. L. Arnold, N. Sri Namachchivaya, K.R. Schenk-Hoppe, Toward an understanding of stochastic Hopf bifurcation: a case study, Int. J. Bifurcation Chaos 6(11) (1996) 1947-1975.
4. S.T. Ariaratnam, Stochastic bifurcation: an illustrate example, in: Wei-Zang Chien et al. (Eds), Proc. 2nd Int. Conf. Nonlinear Mechanics, Peking University Press, Beijing, 1993.
5. K.R. Schenk-Hoppe, Bifurcation scenarios of the noisy Duffing-van der Pol oscillator, Nonlinear Dyn. 11 (1996) 255-274.
6. R.Z. Khasminskii, On the averaging principle for stochastic differential equation, Kibernetika 4 (1968) 260-279 (in Russian).
7. W.Q. Zhu, Y.Q. Yang, Stochastic averaging of quasi-non-integrable-Hamiltonian systems, J. Appl. Mech. ASME 64 (1997) 157-164.
8. Y.K. Lin, G.Q. Cai, Probabilistic Structural Dynamics: Advanced Theory and Applications, McGraw-Hill, New York, 1995.
9. Y.K. Lin, G.Q. Cai, Stochastic stability of non-linear systems, Int. J. Non-Linear Mech. 29(4) (1994) 539-553.
10. W.Q. Zhu, Z.L. Huang, Stochastic stability of quasi-non-integrable-Hamiltonian systems, to appear in J. Sound Vibr.
11. W.Q. Zhu, Y.K. Lin, Stochastic averaging of energy envelope, J. Engng Mech. ASCE 117(8) (1991) 1890-1905.