For citation:
Mchedlova E. S. Analytical approach to complicated dynamics of parametric oscillator. Izvestiya VUZ. Applied Nonlinear Dynamics, 1993, vol. 1, iss. 3, pp. 125-128.
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Russian
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Article
UDC:
53.01.072:517.9
Analytical approach to complicated dynamics of parametric oscillator
Autors:
Mchedlova Elena Sumbatovna, Saratov State University
Abstract:
Behaviour of the nonlinear parametric oscillator is investigated analytically by Melnikov's method. Presented in the paper, the functional dependence gives the boundary of region in parametre space of system, where a complicated dynamics is possible.
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Acknowledgments:
The author expresses deep gratitude to Professor Dmitry Ivanovich Trubetskov, to whom he owes the choice of an interesting research topic, for useful comments made during the work and upon its completion. The author considers it his pleasant duty to express gratitude to the reviewer for valuable comments that contributed to a significant improvement of the article.
Reference:
- Melnikov VК. On the stability of the centre during periodic disturbances. Proc. Moscow Math. Soc. 1963;12:3-52.
- Gaponov-Grekhov АV, Rabinovich МI. Nonlinear physics, stochasticity and structures. Preprint Institute of Applied Physics No. 87. 1983.
- Afraimovich VS, Rabinovich МI, Ugodnikov АD. About the birth of a strange attractor in systems close to Hamiltonian ones. Radiophys. Quantum Electron. 1984;27(10):1346-1349.
- Rabinovich МI, Trubetskov DI. Introduction to the Theory of Oscillations and Waves. M.: Nauka; 1992. 432 p.
- Lichtenberg АJ, Lieberman MA. Regular and Stochastic Motion. N.Y.: Springer; 1983. 499 p. DOI: 10.1007/978-1-4757-4257-2.
- Moon FC. Chaotic Vibrations: An Introduction for Applied Scientists and Engineers. Weinheim: Wiley;1987. 309 p.
Received:
01.10.1992
Accepted:
10.04.1993
Published:
12.01.1994
Journal issue:
- 78 reads