NONLINEAR SYSTEMS WITH FAST AND SLOW MOTIONS. THE CHANGE OF THE PROBABILITY DISTRIBUTION OF FAST MOTIONS INFLUENCED BY SLOW ONES
Cite this article as:
Landa P. S., Ushakov V. G. NONLINEAR SYSTEMS WITH FAST AND SLOW MOTIONS. THE CHANGE OF THE PROBABILITY DISTRIBUTION OF FAST MOTIONS INFLUENCED BY SLOW ONES. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 1, pp. 99-111. DOI: https://doi.org/10.18500/0869-6632-2013-21-1-99-111
The influence of slow processes (random or regular) on the probability distribution of fast random processes is considered. We show that such influence is universal for all random processes, and in some cases this universality is of the multifractal character. As an example we consider stochastic resonance.
1. Jenkins J.H., Fischbach E., Buncher J.B., Gruenwald J.T., Krause D.E., Mattes J.J. Evidence of correlations between nuclear decay rates and Earth-Sun distance // Astroparticle Physics. 2009. Vol. 32. P. 42.
2. Cramer J.G. Radioactive Decay and the Earth-Sun Distance // Analog Science Fiction & Fact Magazine. 2009, Vol. 129.
3. Vlasov Е.В., Гиневский А.С. Генерация и подавление турбулентности в осе-симметричной турбулентной струе при акустическом воздействии // Механика жидкости и газа. 1973, No 6. С. 37.
4. Landa P.S., Ginevsky A.S. Control of Turbulence in Jets by Acoustic Means // Proc. Int. Conf. Physics and Control, St. Petersburg, IEEE, 2003. P. 372.
5. Landa P.S. Regular and Chaotic Oscillations. Berlin-Heidelberg: Springer-Verlag, 2001.
6. Ланда П.С. Механизм стохастического резонанса // ДАН. 2004. Т. 399, No 4. С. 1.
7. Ланда П.С., Власов В.А. Аналитическое рассмотрение влияния космическихфакторов на флуктуации скоростей броуновских частиц // Изв. вузов ПНД. 2011. Т. 19, No 2. C. 56.
8. Шноль С.Э., Ланда П.С., Власов В.А. Влияние космических факторов на скорость альфа-распада // Вестник научно-технического развития. 2011. Т. 42, No 2. С. 1.
9. Шноль С.Э. Космофизические факторы в случайных процессах. Svenska Fisikarkivet, 2009.
10. Блехман И.И. Вибрационная механика. М.: Наука, 1994. 400 с.
11. Дыхне А.М., Крайнов В.П. Быстрые и медленные подсистемы в атомной физике. Азбука, 2002. 217 с.
12. Vlasov Ye.V. and Ginevsky A.S. Acoustic modification of the aerodynamic characteristics of a turbulent jet // Fluid Dynamics. 1967. Vol. 2, No 4. P. 93.
13. Landa P.S., Ushakov V., Kurths J. Rigorous theory of stochastic resonance in overdamped bistable oscillators for weak signals // Chaos, Solitons & Fractals. 2006. Vol. 30. P. 574.
14. Mandelbrot B.B. Fractals: Form, Chance and Dimension. San Francisco: Freeman Comp., 1977.
15. Mandelbrot B.B. and Freeman W.H. The Fractal Geometry of Nature. San Francisco: Freeman Comp., 1983.
16. Nicolis G. and Nicolis C. Stochastic aspects of climate transitions and additive fluctuations // Tellus. 1981. Vol. 33. P. 225.
17. Неймарк Ю.И. Математическое моделирование как наука и искусство. Н.Новгород: Изд-во Нижегородского университета, 2010.
18. Понтрягин Л.С., Андронов А.А., Витт А.А. О статистическом рассмотрении динамических систем. Андронов А.А. Избранные труды. М.: Изд-во АН СССР, 1956.
BibTeX
author = {Polina S. Landa and V. G. Ushakov},
title = {NONLINEAR SYSTEMS WITH FAST AND SLOW MOTIONS. THE CHANGE OF THE PROBABILITY DISTRIBUTION OF FAST MOTIONS INFLUENCED BY SLOW ONES},
year = {2013},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {21},number = {1},
url = {https://old-andjournal.sgu.ru/en/articles/nonlinear-systems-with-fast-and-slow-motions-the-change-of-the-probability-distribution-of},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2013-21-1-99-111},pages = {99--111},issn = {0869-6632},
keywords = {Probability distribution,random processes,stochastic resonance.},
abstract = {The influence of slow processes (random or regular) on the probability distribution of fast random processes is considered. We show that such influence is universal for all random processes, and in some cases this universality is of the multifractal character. As an example we consider stochastic resonance. }}