Stochastic bifurcations in a bistable Duffing - Van der Pol oscillator with colored noise

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 83, Issue 5, 2011, Pages

  Xu, Yong ^a   Gu, Rencai ^a   Zhang, Huiqing ^a   Xu, Wei ^a   Duan, Jinqiao ^b  

^a NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

^b Illinois Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION PARAMETER; BISTABLES; COLORED NOISE; CORRELATION TIME; DUFFING-VAN DER POL OSCILLATOR; GAUSSIANS; LARGEST LYAPUNOV EXPONENT; MULTIPLICATIVE NOISE; NOISE CORRELATION; NOISE INTENSITIES; QUALITATIVE CHANGES; STATIONARY PROBABILITY DENSITY FUNCTION; STOCHASTIC AVERAGING METHODS; STOCHASTIC BIFURCATION; VAN DER POL OSCILLATOR;

BIFURCATION (MATHEMATICS); CIRCUIT OSCILLATIONS; DENSITY FUNCTIONAL THEORY; LYAPUNOV METHODS; MULTIUSER DETECTION; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; STOCHASTIC SYSTEMS; WHITE NOISE;

OSCILLATORS (MECHANICAL);

EID: 79961060272     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.83.056215     Document Type: Article

References (27)

1. O. V. Ushakov, H. J. Wünsche, F. Henneberger, I. A. Khovanov, L. Schimansky-Geier, and M. A. Zaks, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.123903 95, 123903 (2005). (Pubitemid 41505645)
2. R. Mankin, T. Laas, A. Sauga, A. Ainsaar, and E. Reiter, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.74.021101 74, 021101 (2006). (Pubitemid 44172613)
3. Y. K. Lin and G. Q. Cai, Probabilistic Structure Dynamic: Advanced Theory and Applications (McGraw-Hill, New York, 1995).
4. N. Sri Namachchivaya and W. M. Tien, J. Fluids Struct. 0889-9746 10.1016/S0889-9746(89)90157-6 3, 609 (1989).
5. N. Sri Namachchivaya, Appl. Math. Comput. 0096-3003 10.1016/0096-3003(90) 90051-4 38, 101 (1990).
6. L. Billings, I. Schwartz, D. Morgan, E. Bollt, R. Meucci, and E. Allaria, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.70.026220 70, 026220 (2004).
7. W. Xu, Q. He, T. Fang, and H. Rong, Int. J. Non-Linear Mech. 0020-7462 10.1016/j.ijnonlinmec.2004.02.009 39, 1473 (2004).
8. Q. He, W. Xu, H. Rong, and T. Fang, Physica A 0378-4371 10.1016/j.physa.2004.01.067 338, 319 (2004).
9. C. Chiarella, X. Zhong He, D. Wang, and M. Zheng, Physica A 0378-4371 10.1016/j.physa.2008.01.078 387, 3837 (2008).
10. S. Wieczorek, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.036209 79, 036209 (2009).
11. H. Nakao, J. N. Teramae, D. S. Goldobin, and Y. Kuramoto, Chaos 1054-1500 10.1063/1.3488977 20, 033126 (2010).
12. D. S. Goldobin and A. Pikovsky, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.71.045201 71, 045201 (R) (2005). (Pubitemid 40619602)
13. A. Zakharova, T. Vadivasova, V. Anishchenko, A. Koseska, and J. Kurths, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.011106 81, 011106 (2010).
14. H. Hasegawa, Physica D 0167-2789 10.1016/j.physd.2007.08.009 237, 137 (2008). (Pubitemid 351163409)
15. L. Arnold, Random Dynamical Systems (Springer, New York, 1998).
16. D. S. Goldobin, J.-n. Teramae, H. Nakao, and G. B. Ermentrout, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.154101 105, 154101 (2010).
17. D. S. Goldobin and A. Pikovsky, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.73.061906 73, 061906 (2006). (Pubitemid 43877887)
18. A. Drozd-Rzoska, S. J. Rzoska, and J. Zioło, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.61.5349 61, 5349 (2000).
19. C. R. Doering and J. C. Gadoua, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.2318 69, 2318 (1992).
20. P. Holmes and D. Rand, Int. J. Non-Linear Mech. 0020-7462 10.1016/0020-7462(80)90031-1 15, 449 (1980).
21. J. Guckenheimer and P. Holmes, Nonlinear Oscillation Dynamical Systems and Bifurcation of Vector Fields (Springer, Berlin, 1983).
22. W. Zhu, Appl. Mech. Rev. 0003-6900 10.1115/1.3101980 49, S72 (1996).
23. J. Roberts and P. Spanos, Int. J. Non-Linear Mech. 0020-7462 10.1016/0020-7462(86)90025-9 21, 111 (1986).
24. W. Horsthemke and R. Lefever, Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology, 2nd ed. (Springer-Verlag, Berlin/Heidelberg, 2007).
25. R. L. Honeycutt, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.45.604 45, 604 (1992).
26. G. Benettin, L. Galgani, and A. Giorgilli, Meccanica 0025-6455 10.1007/BF02128237 15, 21 (1980).
27. L. Arnold, P. Imkeller, and N. Sri Namachchivaya, J. Sound Vib. 0022-460X 10.1016/S0022-460X(03)00211-6 269, 1003 (2004).