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

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Landa P. S. Excitation of chaotic and stochastic oscillations in different systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 1, pp. 3-11. DOI: 10.18500/0869-6632-2010-18-1-3-11

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Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
537.86/87:530.182
DOI: 
10.18500/0869-6632-2010-18-1-3-11

Excitation of chaotic and stochastic oscillations in different systems

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

A possible response of both lumped and distributed systems to weak random disturbances of forced character (additive) and the disturbances leading to parametric excitation of oscillations (multiplicative) is presented. It is shown that multiplicative disturbances of a system may cause radical change in its behavior, similar to that occurs in thermodynamically equilibrium systems after second kind phase transitions.

Key words: 
Additive and multiplicative random perturbations
excitation of oscillations
non-equilibrium phase transitions of the second order
Reference: 
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  4. Stratonovich RL. Selected Problems of Fluctuation Theory in Radio Engineering. Moscow: Sov. radio; 1961. (in Russian).
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  7. Landa PS. Onset of turbulence in open liquid flows as a nonequilibrium noise-induced second-order phase transition. Technical Physics. 1998;43(1):27–34. DOI: 10.1134/1.1258930.
  8. Landa PS, Zaikin AA. Nonequilibrium noise-induced phase transitions in simple systems. J. Exp. Theor. Phys. 1997;84:197–208. DOI: 10.1134/1.558137.
  9. Landa PS, Zaikin AA. Noise-induced phase transitions in nonlinear oscillators. AIP Conference Proceedings 465 (Computing Anticipatory Systems, CASYS’98, Liege, Belgium). 1998:419–433.
  10. Landa PS. Regular and Chaotic Oscillations. Berlin-Heidelberg: Springer-Verlag; 2001.
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  12. Landa PS. Self-Oscillation in Systems with Finite Number of Degress of Freedom. Moscow: Nauka; 1980. (in Russian)
  13. Landa PS, Zaikin AA. Noise-induced phase transitions in a pendulum with a randomly vibrating suspension axis. Phys. Rev. E. 1996;54(4):3535–3544. DOI: 10.1103/physreve.54.3535.
  14. Landa PS. Nonlinear Oscillations and Waves. Moscow: Fizmatlit; 1997. (in Russian). 
  15. Landa PS, McClintock PVE. Development of turbulence in subsonic submerged jets. Phys. Rep. 2004;397:1–62. DOI: 10.1016/j.physrep.2004.03.004.
  16. Landa PS, Trubetskov DI, Gusev VA. Delusions versus reality in some physics problems: theory and experiment.  Phys. Usp. 2009;52(3):235–255.
Received: 
17.03.2009
Accepted: 
05.10.2009
Published: 
31.03.2010
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