Analysis of period-doubling bifurcation in double-well stochastic Duffing system via Laguerre polynomial approximation

Nonlinear Dynamics

Volumn 52, Issue 3, 2008, Pages 289-299

  Ma, S J ^a   Xu, W ^a   Fang, T ^a  

^a NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

Author keywords

Double well Duffing system; Exponential probability density function; Laguerre polynomial approximation; Stochastic period doubling bifurcation

Indexed keywords

ASYMPTOTIC STABILITY; HARMONIC ANALYSIS; NUMERICAL METHODS; POLYNOMIAL APPROXIMATION; PROBABILITY DENSITY FUNCTION; STOCHASTIC MODELS;

DOUBLE-WELL DUFFING SYSTEMS; EXPONENTIAL PROBABILITY DENSITY FUNCTIONS; LAGUERRE POLYNOMIAL APPROXIMATION; STOCHASTIC PERIOD-DOUBLING BIFURCATION;

BIFURCATION (MATHEMATICS);

EID: 43349099049     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-007-9278-2     Document Type: Article

References (25)

1. Zhu, W.Q., Huang, Z.L., Suzuki, Y.: Response and stability of strongly non-linear oscillators under wide-band random excitation. Int. J. Non-Linear Mech. 36, 1235-1250 (2001)
2. Rong, H.W., Meng, G., Wang, X.D., Fang, T.: Response of strongly non-linear oscillators to narrowband random excitation. J. Sound Vib. 266, 875-887 (2003)
3. Xu, W., He, Q., Fang, T., Rong, H.W.: Global analysis of stochastic in Duffing system. Int. J. Bifur. Chaos 13, 3115-3123 (2003)
4. Shinozuka, M.: Probability modeling of concrete structures. ASCE J. Eng. Mech. Div. 98, 1433-1451 (1972)
5. Kleiber, M., Hien, T.D.: The Stochastic Finite Element Method: Basic Perturbation Technique and Computer Implementation. Wiley, New York (1992)
6. Ghamem, R., Spans, P.: Stochastic Finite Element: A Spectral Approach. Springer, Berlin (1991)
7. Pettit, C.L., Beran, P.S.: Spectral and multiresolution Wiener expansions of oscillatory stochastic processes. J. Sound Vib. 294, 752-779 (2006)
8. Le Maître, O.P., Najm, H.N., Ghanem, R.G., Knio, O.M.: Multi-resolution analysis of Wiener-type uncertainty propagation schemes. J. Comput. Phys. 197, 502-531 (2004)
9. Le Maître, O.P., Knio, O.M., Najm, H.N., Ghanem, R.G.: Uncertainty propagation using Wiener-Haar expansions. J. Comput. Phys. 197, 28-57 (2004)
10. Xiu, D.B., Karniadakis, G.E.: Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Comput. Methods Appl. Mech. Eng. 191, 4927-4948 (2002)
11. Wan, X.L., Karniadakis, G.E.: An adaptive multi-element generalized polynomial chaos method for stochastic differential equations. J. Comput. Phys. 209, 617-642 (2005)
12. Fang, T., Leng, X.L., Song, C.Q.: Chebyshev polynomial approximation for dynamical response problem of random system. J. Sound Vib. 226, 198-206 (2003)
13. Leng, X.L., Wu, C.L., Ma, X.P., Meng, G., Fang, T.: Bifurcation and chaos analysis of stochastic Duffing system under harmonic excitations. Nonlinear Dyn. 42, 185-198 (2005)
14. Ma, S.J., Xu, W., Li, W., Fang, T.: Analysis of stochastic bifurcation and chaos in stochastic Duffing-van der Pol system via Chebyshev polynomial approximation. Chin. Phys. 15, 1231-1238 (2006)
15. Guckenheimer, J., Holmes, P.J.: Nonlinear Oscillators, Dynamical System and Bifurcation of Vector Fields. Springer, New York (1983)
16. Holmes, P.: A nonlinear oscillator with a strange attractor. Philos. Trans. Roy. Soc. Lond. Ser. A 292, 419-448 (1979)
17. Moon, F.C., Homles, P.J.: A megnetoelastic strange attractor. J. Sound Vib. 65, 275-296 (1979)
18. Osipov, G., Glatz, L., Troger, H.: Suppressing chaos in the Duffing oscillator by impulsive actions. Chaos Solitons Fractals 9, 307-321 (1998)
19. Litvak-Hinenzon, A., Rom-Kedar, V.: Symmetry-breaking perturbations and strange attractors. Phys. Rev. E 55, 4964-4978 (1997)
20. Chacón, R., García-Hoz, A.M.: Bifurcation and chaos in a parametrically damped double-well Duffing oscillator subjected to symmetric periodic pulses. Phys. Rev. E 59, 6558-6568 (1999)
21. Kim, S.Y., Kim, Y.: Dynamic stabilization in the double-well Duffing oscillator. Phys. Rev. E 61, 6517-6520 (2000)
22. Szmplińskia-Stupnicka, W., Zubrzycki, A., Tyrkiel, E.: New phenomena in the neighborhood of the codimension-two bifurcation in the twin-well Duffing oscillator. Int. J. Bifur. Chaos 10, 1367-1381 (2000)
23. Borwein, P., Erdélyi, T.: Polynomials and Polynomial Inequality. Springer, New York (1995)
24. Kamerich, E.: A Guide to Maple. Springer, New York (1999)
25. Hu, H.Y.: Symmetry and bifurcation of the periodic response of an externally forced nonlinear oscillator. J. Vib. Eng. S 7, 26-36 (1994)