Stochastic period-doubling bifurcation in biharmonic driven Duffing system with random parameter

Chinese Physics B

Volumn 17, Issue 3, 2008, Pages 857-864

  Xu, Wei ^a   Ma, Shao Juan ^a   Xie, Wen Xian ^a  

^a NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

Author keywords

Orthogonal polynomial approximation; Random parameter; Stochastic Duffing system; Stochastic period doubling bifurcation

Indexed keywords

BIFURCATION (MATHEMATICS); HARMONIC ANALYSIS; PARAMETER ESTIMATION; POLYNOMIAL APPROXIMATION;

ORTHOGONAL POLYNOMIAL APPROXIMATION; RANDOM PARAMETER; STOCHASTIC DUFFING SYSTEM; STOCHASTIC PERIOD-DOUBLING BIFURCATION;

RANDOM PROCESSES;

EID: 42449158046     PISSN: 16741056     EISSN: None     Source Type: Journal    
DOI: 10.1088/1674-1056/17/3/022     Document Type: Article

References (30)

1. Guckenheimer J and Holmes P J 1983 Nonlinear Oscillators, Dynamical System and Bifurcation of Vector Fields (New York: Springer)
2. Parlitz U and Lauterborn W 1985 Phys. Lett. A 107 351
3. Fang T and Dowell E H 1987 Int. J. Non-Linear Mech. 22 401
4. Wiggins S 1987 Phys. Lett. A 124 138
5. Nayfeh A H and Nestor E S 1989 Int. J. Non-Linear Mech. 24 483
6. Venkatesan A, Lakshmanan M, Prasad A and Ra-maswamy R 2000 Phys. Rev. E 61 3641
7. Qu Z L, Hu G, Yang G J and Qin G G 1995 Phys. Rev. Lett. 74 1736
8. Yang J Z, Qu Z L and Hu G 1996 Phys. Rev. E 53 4402
9. Lashman M and Mertzios K 1996 Chaos in Nonlinear Oscillators-Controlling and Synchronization (Singapore: World Scientific)
10. Yagasaki K and Uozumi T 1998 Phys. Lett. A 247 129
11. Chacón R 1999 Phys. Lett. A 257 293
12. Wang R Q, Deng J and Jing Z J 2006 Chaos, Solitons Fractals 27 249
13. Venkatesan A, Parthasarathy S and Lakshmanan M 2003 Chaos, Solitons Fractals 18 891
14. Jing Z J and Wang R Q 2005 Chaos, Solitons Fractals 23 399
15. Jing Z J, Huang J C and Deng J 2007 Chaos, Solitons Fractals 33 795
16. Shinozuka M 1972 J. Eng. Mech. Dive. ASCE 98 1433
17. Kleiber M and Hien T D 1992 The Stochastic Finite Element Method: Basic Perturbation Technique and Computer Implementation (New York: Wiley)
18. Ghamem R and Spans P 1991 Stochastic Finite Element: a Spectral Approach (Berlin: Springer)
19. Pettit C L and Beran P S 2006 J. Sound Vib. 294 752
20. Le Matre O P, Najm H N, Ghanem R G and Knio O M 2004 J. Comput. Phys. 197 502
21. Xiu D B and Karniadakis G E 2002 Comput. Methods Appl. Mech. Engng. 191 4927
22. Wan X L and Karniadakis G E 2005 J. Comput. Phys. 209 617
23. Ma S J, Xu W, Li W and Jin Y F 2005 Acta Phys. Sin. 54 3508 (in Chinese)
24. Leng X L, Wu C L, Ma X P and Fang T 2005 Nonlinear Dynamics 42 185
25. Ma S J, Xu W, Li W and Fang T 2006 Chin. Phys. 15 1231
26. Ma S J, Xu W and Li W 2006 Acta Phys. Sin. 55 4013 (in Chinese)
27. Wu C L, Lei Y M and Fang T 2006 Chaos, Solitons Fractals 27 459
28. Wu C L, Fang T and Rong H W 2007 Chaos, Solitons Fractals 32 1201
29. Borwein P and Erdélyi T 1995 Polynomials and Polynomial Inequality (New York: Springer)
30. Kamerich E 1999 A Guide to Maple (New York: Springer)