SELF-­SUSTAINED OSCILLATIONS IN QUASIHARMONIC AND CHAOTIC OSCILLATORS IN THE PRESENCE OF FLUCTUATIONS

Cite this article as:

Anishenko V. S., Vadivasova Т. Е., Strelkova G. I. SELF-­SUSTAINED OSCILLATIONS IN QUASIHARMONIC AND CHAOTIC OSCILLATORS IN THE PRESENCE OF FLUCTUATIONS. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 4, pp. 114-126. DOI: https://doi.org/10.18500/0869-6632-2009-17-4-114-126

The paper presents the results of the classical theory of fluctuations in the quasiharmonic van der Pol oscillator. Stochastic equations for amplitude and phase of selfsustained oscillations are formulated and then their solutions are analyzed. The autocorrelation function and power spectrum of noisy self­sustained oscillations are studied. Then the spectral and correlations characteristics of chaotic self­sustained oscillations are numerically analyzed in spiral chaos oscillators. Statistical characteristics of spiral chaos are explored both without and in the presence of fluctuations, and the obtained results are compared with the classical theory of fluctuations in the van der Pol oscillator.

Authors: 
Anishenko Vadim S., Saratov State University, ul. Astrakhanskaya, 83, Saratov, 410012, Russia , wadim@chaos.ssu.runet.ru
Vadivasova Т. Е., Saratov State University, ul. Astrakhanskaya, 83, Saratov, 410012, Russia , VadivasovaTE@yandex.ru
Strelkova G. I., Saratov State University, ul. Astrakhanskaya, 83, Saratov, 410012, Russia , strelkovagi@info.sgu.ru
Key words: 
Spiral attractor, noisy self­sustained oscillations, harmonic noise, correlation time, spectral line width.
DOI: 
10.18500/0869-6632-2009-17-4-114-126
Literature

1. Стратонович Р.Л. Избранные вопросы теории флуктуаций в радиотехнике. М.: Сов. радио, 1961.

2. Анищенко В.С., Вадивасова Т.Е., Окрокверцхов Г.А., Стрелкова Г.И. Статистические свойства динамического хаоса // УФН. 2005. Т. 175, No 2. С. 163.

3. Анищенко В.С., Астахов В.В., Вадивасова Т.Е. Регулярные и хаотические автоколебания. Синхронизация и влияние флуктуаций. М.: Интеллект, 2009.

Heading: 
Review of Actual Problems of Nonlinear Dynamics
Status: 
одобрено к публикации
Short Text (PDF): 
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Full Text (PDF): 
2009no4p114.pdf

BibTeX

@article{Анищенко -IzvVUZ_AND-17-4-114,
author = {Vadim S. Anishenko and Т. Е. Vadivasova and G. I. Strelkova},
title = {SELF-­SUSTAINED OSCILLATIONS IN QUASIHARMONIC AND CHAOTIC OSCILLATORS IN THE PRESENCE OF FLUCTUATIONS},
year = {2009},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {17},number = {4},
url = {https://old-andjournal.sgu.ru/en/articles/self-sustained-oscillations-in-quasiharmonic-and-chaotic-oscillators-in-the-presence-of},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2009-17-4-114-126},pages = {114--126},issn = {0869-6632},
keywords = {Spiral attractor,noisy self­sustained oscillations,harmonic noise,correlation time,spectral line width.},
abstract = {The paper presents the results of the classical theory of fluctuations in the quasiharmonic van der Pol oscillator. Stochastic equations for amplitude and phase of selfsustained oscillations are formulated and then their solutions are analyzed. The autocorrelation function and power spectrum of noisy self­sustained oscillations are studied. Then the spectral and correlations characteristics of chaotic self­sustained oscillations are numerically analyzed in spiral chaos oscillators. Statistical characteristics of spiral chaos are explored both without and in the presence of fluctuations, and the obtained results are compared with the classical theory of fluctuations in the van der Pol oscillator. }}