NOISE-INDUCED BIFURCATIONS IN BISTABLE OSCILLATOR


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Vadivasova Т. Е., Zakharova А. S., Anishenko V. S. NOISE-INDUCED BIFURCATIONS IN BISTABLE OSCILLATOR. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 2, pp. 114-122. DOI: https://doi.org/10.18500/0869-6632-2009-17-2-114-122


We investigate bistable oscillator under the influence of additive, white and colored, noise. We have found noise-induced bifurcations that consist in a qualitative change of stationary distribution of oscillations amplitude. In the region of bimodal distribution the effect of coherent resonance takes place both for white and colored noise.

DOI: 
10.18500/0869-6632-2009-17-2-114-122
Literature

1. Хорстхемке В., Лефевр Р. Индуцированные шумом переходы. М.: Мир, 1987.

2. Bulsara A.R., Schieve W.C., Gragg R.F. Phase transitions induced by white noise in bistable optical systems // Phys. Lett. A. 1978. Vol. 68. P. 294.

3. Анищенко В.С., Сафонова М.А. Индуцированное шумом экспоненциальное разбегание фазовых траекторий в окрестности регулярных аттракторов // Письма в ЖТФ. 1986. Т. 12, No 12. С. 740.

4. Sigeti D., Horsthemke W. Pseudo-regular oscillations induced by external noise // J.Stat.Phys. 1989. Vol. 54. P. 1217.

5. Schimansky-Geier L., Herzel H. Positive Lyapunov exponents in the Kramers oscillator // Journal of Statistical Physiks. 1993. Vol. 70. P. 141.

6. Armbruster D., Stone E., Kirk V. Noisy heterodinic networks // Chaos. 2003. Vol. 13, No 1. P. 71.

7. Finn J.M., Tracy E.R., Cooke W.E. and Richardson A.S. Noise stabilised random attractor // Phys. Rev. E. 2006. Vol. 73. P. 026220(12).

8. Arnold L. Random Dynamical System. Springer, Berlin, 2003.

9. Ushakov O.V.,Wunsche H.-J., et al. ` Coherence resonance near a Hopf bifurcation // Phys. Rev. Lett. 2005. Vol. 95, 123903(4).

10. Ланда П.С. Автоколебания в системах с конечным числом степеней свободы. М.: Наука, 1980.

11. Стратонович Р.Л. Избранные вопросы теории флуктуаций в радиотехнике. М.: Сов. радио, 1961.

12. Вентцель А.Д., Фрейдлин М.И. Флуктуации в динамических системах под действием малых случайных возмущений. М.: Наука, 1979.

13. Pikovsky A., Kurths J. Coherence resonance in a noisy driven excitable system // Phys. Rev. Lett. 1997. Vol. 78. P. 775.

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BibTeX

@article{Вадивасова-IzvVUZ_AND-17-2-114,
author = {Т. Е. Vadivasova and А. S. Zakharova and Vadim S. Anishenko},
title = {NOISE-INDUCED BIFURCATIONS IN BISTABLE OSCILLATOR},
year = {2009},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {17},number = {2},
url = {https://old-andjournal.sgu.ru/en/articles/noise-induced-bifurcations-in-bistable-oscillator},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2009-17-2-114-122},pages = {114--122},issn = {0869-6632},
keywords = {Noise influence,stochastic bifurcation,bistable oscillator,coherent resonance.},
abstract = {We investigate bistable oscillator under the influence of additive, white and colored, noise. We have found noise-induced bifurcations that consist in a qualitative change of stationary distribution of oscillations amplitude. In the region of bimodal distribution the effect of coherent resonance takes place both for white and colored noise. }}