Mass-dependent instability of an oscillator with additive and multiplicative random forces

M. Gitterman; D. Kessler

doi:10.1063/1.4825913

Mass-dependent instability of an oscillator with additive and multiplicative random forces

M. Gitterman
, D. Kessler

Department of Physics - at Bar-Ilan University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

We study the instability of a harmonic oscillator subject to additive and dichotomous multpicalive noise, focusing on the dependence of the instability threshold on the mass. For multiplicative noise in the damping, the energy instability threshold is crossed as the mass is decreased, as long as the smaller damping is in fact negative. For multiplicative noise in the stifness, the situation is more complicate and in fact the energy transition is reentrant for intermidiate noise strength and damping. For multiplicative noise of the mass, taking the velocity to be conserved as the mass is changed, we find that increasing the mass destabilizes the system.

Original language	English
Title of host publication	11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013
Pages	1940-1942
Number of pages	3
DOIs	https://doi.org/10.1063/1.4825913
State	Published - 2013
Event	11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013 - Rhodes, Greece Duration: 21 Sep 2013 → 27 Sep 2013

Publication series

Name	AIP Conference Proceedings
Volume	1558
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013
Country/Territory	Greece
City	Rhodes
Period	21/09/13 → 27/09/13

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 7 Affordable and Clean Energy

Keywords

energy instability
multiplicative noise

Access to Document

10.1063/1.4825913

Cite this

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title = "Mass-dependent instability of an oscillator with additive and multiplicative random forces",

abstract = "We study the instability of a harmonic oscillator subject to additive and dichotomous multpicalive noise, focusing on the dependence of the instability threshold on the mass. For multiplicative noise in the damping, the energy instability threshold is crossed as the mass is decreased, as long as the smaller damping is in fact negative. For multiplicative noise in the stifness, the situation is more complicate and in fact the energy transition is reentrant for intermidiate noise strength and damping. For multiplicative noise of the mass, taking the velocity to be conserved as the mass is changed, we find that increasing the mass destabilizes the system.",

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Gitterman, M & Kessler, D 2013, Mass-dependent instability of an oscillator with additive and multiplicative random forces. in 11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013. AIP Conference Proceedings, vol. 1558, pp. 1940-1942, 11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013, Rhodes, Greece, 21/09/13. https://doi.org/10.1063/1.4825913

Mass-dependent instability of an oscillator with additive and multiplicative random forces. / Gitterman, M.; Kessler, D.
11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013. 2013. p. 1940-1942 (AIP Conference Proceedings; Vol. 1558).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - We study the instability of a harmonic oscillator subject to additive and dichotomous multpicalive noise, focusing on the dependence of the instability threshold on the mass. For multiplicative noise in the damping, the energy instability threshold is crossed as the mass is decreased, as long as the smaller damping is in fact negative. For multiplicative noise in the stifness, the situation is more complicate and in fact the energy transition is reentrant for intermidiate noise strength and damping. For multiplicative noise of the mass, taking the velocity to be conserved as the mass is changed, we find that increasing the mass destabilizes the system.

AB - We study the instability of a harmonic oscillator subject to additive and dichotomous multpicalive noise, focusing on the dependence of the instability threshold on the mass. For multiplicative noise in the damping, the energy instability threshold is crossed as the mass is decreased, as long as the smaller damping is in fact negative. For multiplicative noise in the stifness, the situation is more complicate and in fact the energy transition is reentrant for intermidiate noise strength and damping. For multiplicative noise of the mass, taking the velocity to be conserved as the mass is changed, we find that increasing the mass destabilizes the system.

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ER -

Mass-dependent instability of an oscillator with additive and multiplicative random forces

Abstract

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UN SDGs

Keywords

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