ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


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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: 10.18500/0869-6632-2013-21-1-99-111

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Language: 
Russian
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Article
UDC: 
534;53.03;519.213

Nonlinear systems with fast and slow motions. The change of the probability distribution of fast motions influenced by slow ones

Autors: 
Landa Polina Solomonovna, Lomonosov Moscow State University
Ushakov Vadim Gennadevich, Lomonosov Moscow State University
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

Reference: 
  1. Jenkins JH, Fischbach E, Buncher JB, Gruenwald JT, Krause DE, Mattes JJ. Evidence of correlations between nuclear decay rates and Earth-Sun distance. Astroparticle Physics. 2009;32(1):42–46. DOI:10.1016/j.astropartphys.2009.05.004
  2. Cramer JG. Radioactive Decay and the Earth-Sun Distance. Analog Science Fiction & Fact Magazine. 2009;129(5).
  3. Vlasov EV, Ginevskii AS. Generation and suppression of turbulence in an axisymmetric turbulent jet under an acoustic effect. Fluid Dyn. 1973;8(6):881–885. DOI: 10.1007/BF01014260.
  4. Landa PS, Ginevsky AS. Control of Turbulence in Jets by Acoustic Means. Proc. Int. Conf. Physics and Control. St. Petersburg: IEEE; 2003. p. 372. DOI: 10.1109/PHYCON.2003.1236780
  5. Landa PS. Regular and Chaotic Oscillations. Berlin-Heidelberg: Springer-Verlag; 2001. 400 p.
  6. Landa PS. MECHANISM OF STOCHASTIC RESONANCE. DAS. 2004;399(4):477–480.
  7. Landa PS, Vlasov VA. Analytical consideration of the cosmic factor effects upon the fluctuations of brown particle velocities. Izvestiya VUZ. Applied Nonlinear Dynamics. 2011;19(2):56-68. DOI: 10.18500/0869-6632-2011-19-2-56-68
  8. Shnol SE, Landa PS, Vlasov VA. Influence of cosmic factors on alpha decay speed. Vestnik nauchno-tehnicheskogo razvitiya. 2011;42(2):23–45.
  9. Shnol SE. Cosmophysical factors in random processes. Stockholm: Svenska Fisikarkivet; 2009. 388 p. (In Russian).
  10. Blechman AI. Vibration mechanics. Moscow: Nauka; 1994. 400 p. (In Russian).
  11. Dihne AM, Krainov VP. Fast and slow subsystems in atomic physics. Moscow: Azbooka; 2002. 217 p. (In Russian).
  12. Vlasov YeV, Ginevsky AS. Acoustic modification of the aerodynamic characteristics of a turbulent jet. Fluid Dynamics. 1967;2(4):93–96. DOI:10.1007/BF01019549
  13. Landa PS, Ushakov V, Kurths J. Rigorous theory of stochastic resonance in overdamped bistable oscillators for weak signals. Chaos, Solitons & Fractals. 2006; 30(3):574–578. DOI:10.1016/j.chaos.2005.08.116
  14. Mandelbrot BB. Fractals: Form, Chance and Dimension. San Francisco: Freeman Comp.; 1977. 365 p.
  15. Mandelbrot BB, Freeman WH. The Fractal Geometry of Nature. San Francisco: Freeman Comp.; 1983. 460 p.
  16. Nicolis G, Nicolis C. Stochastic aspects of climate transitions and additive fluctuations. Tellus. 1981;33(3):225–234. DOI: 10.1111/j.2153-3490.1981.tb01746.x
  17. Neymark UI. Mathematical modeling as science and art.Nizhni Novgorod: Nizhni Novgorod University Press; 2010. 420 p. (In Russian).
  18. Pontryagin LS, Andronov AA, Witt AA. On statistical review of dynamic systems. Andronov A.A. Selected works. Moscow: Nauka; 1956. 538 p. (In Russian).
Received: 
05.10.2012
Accepted: 
05.10.2012
Published: 
31.05.2013
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