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

For citation:

Landa P. S. One more on universality of oscillatory and wave processes. Foundations for construction of mathematical models. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 3, pp. 119-126. DOI: 10.18500/0869-6632-2013-21-3-119-126

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 15_landa.pdf
(downloads: 158)
Language: 
Russian
Heading: 
Methodical Papers on Nonlinear Dynamics
Article type: 
Article
UDC: 
534
DOI: 
10.18500/0869-6632-2013-21-3-119-126

One more on universality of oscillatory and wave processes. Foundations for construction of mathematical models

Autors: 
Landa Polina Solomonovna, Lomonosov Moscow State University
Abstract: 

Nonlinear systems with random sources are considered. As a rule, such systems cannot be solved both analytically and numerically. But due to the universality of the oscillation theory we can use simple models and obtain qualitative results.

Key words: 
Universality of oscillatory and wave processes
stochastic resonance
mathematical models
unsolvable problems
Reference: 
  1. Shnol SE. Cosmophysical factors in random processes. Ed. Rabunskiy DD. Stockholm: Svenska Fysikarkivаt; 2009. 388 p. (In Russian).
  2. Mandelstam LI. Lectures on oscillations. V.4. Moscow: AS USSR; 1955. 504 p. (In Russian).
  3. Strelkov SP. Introduction to the theory of oscillation. St. Petersburg: Lan; 2005. 437 p. (In Russian).
  4. Blechman AI. Vibration mechanics. Moscow: Nauka; 1994. 394 p. (In Russian).
  5. Landa PS, Neimark YuI, McClintock PVE. Changes in the effective parameters of averaged motion in nonlinear systems subject to noise. Journal of Statistical Physics. 2006;125(3):593–620. DOI:10.1007/s10955-006-9209-5.
  6. Benzi R, Sutera A, Vulpiani A. The mechanism of stochastic resonance. J. Phys. A: Math. Gen. 1981;14(11):453–457. DOI:10.1088/0305-4470/14/11/006.
  7. 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.
  8. Landa PS. Mehanism of stochastic resonance. DAN. 2004;399(4):477–480.
  9. Landa PS, McClintock PVE. Changes in the dynamical behavior of nonlinear systems induced by noise. Physics Reports. 2000;323(1):1–80. DOI: 10.1016/S0370-1573(99)00043-5.
  10. Modelling the Dynamics of Biological Systems. Eds. Mosekilde E, Mouritsen OG. Berlin: Springer-Verlag; 1995. 294 p.
  11. Gontar V. A new theoretical approach to the description of physico-chemical reaction dynamics with chaotic behavior. Chaos in Chemistry and Biochemistry. Eds. R.J. Field RJ, Gyorgyi. London: World Scientific; 1993. 225 p.
  12. Lotka AJ. Undamped oscillations derived from the law of nass action. J. Amer. Chem. Soc. 1920;42:1595–1599.
  13. Volterra V. Lecons sur la Theorie Mathematique de la Lutte pour la Vie. Paris: Cauthier-Villars; 1931. 214 p.
  14. Landa PS. Nonlinear Oscillations and Waves in Dynamical Systems. Dordrecht-Boston-London: Kluwer Academic Publishers; 1996. 535 p.
  15. Neymark UI. Mathematical model of interaction between manufacturers, products and consumers. Dynamics of systems (dynamics, stochasticity, bifurcation). Gorky: GSU; 1990. 159 p. (In Russian).
  16. Неймарк ЮИ. Mathematical model of the producer-product-manager community. Mathematical modeling as science and art. Nizhny Novgorod: NNUP; 2010. 404 p. (In Russian).
  17. Neymark UI. Salinization of a reservoir with a bay and mysteries of the Caspian Sea. Mathematical modeling as science and art. Nizhny Novgorod: NNUP; 2010. 404 p. (In Russian).
  18. Landa PS. Universality of oscillation theory laws. Types and role of mathematical models. Discrete Dynamics in Nature and Society. 1997;1:99–110. DOI:10.1155/S1026022697000113.
  19. Landa PS, Ginevsky AS. Use mathematical models to solve "unsolvable" problems. Nonlinear problems of oscillation theory and control theory. Vibration mechanics. Ed. Belecky BB, Indeycev DA, Fradkov AL. St. Petersburg: Nauka; 2009. 367 p. (In Russian).
  20. Blumenfeld LA. Solved and unresolved problems of biological physics. Moscow: URSS; 2002. 160 p. (In Russian).
  21. Landa PS, McClintock PVE. Some «non-solvable» problems and methods of their «solution». Vortex separation and a stochastic model of stall flutter. (In Press).
  22. Andronov AA, Witt AA. To the mathematical theory of self-oscillating systems with two degrees of freedom. Technical Physics. 1934;4(1):122–134.
  23. Theodorczyk KF. Self-oscillating systems. Moscow-Leningrad: Tehizdat; 1952. (In Russian).
  24. Skibarko AP, Strelkov SP. Qualitative investigation of processes in the generator according to a complex scheme. To the Van der Paul tightening theory. Technical Physics. 1934;4(1):158–171.
  25. Kurkin AA, Pelinovsky EN. The waves are killers. Nizhny Novgorod: NNUP; 2004. 157 p.(In Russian).
Received: 
24.09.2013
Accepted: 
24.09.2013
Published: 
31.10.2013
Short text (in English):
PDF icon a2013no3p119.pdf
(downloads: 91)
  • 1916 reads