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On the stochastic resonance phenomenon in parametrically excited systems

Part of: Equations and systems with randomness Stochastic analysis Functional-differential and differential-difference equations

Published online by Cambridge University Press:  26 September 2018

VLADISLAV SOROKIN Open the ORCID record for VLADISLAV SOROKIN [Opens in a new window]  and
ILIYA BLEKHMAN
VLADISLAV SOROKIN
Affiliation:
Department of Mechanical Engineering, The University of Auckland, Auckland, New Zealand email: [email protected]
ILIYA BLEKHMAN
Affiliation:
Mekhanobr-Tekhnika Research & Engineering Corp., St. Petersburg, Russia email: [email protected] Institute of Problems in Mechanical Engineering, RAS, St. Petersburg, Russia
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Abstract

The stochastic resonance phenomenon implies “positive” changing of a system behaviour when noise is added to the system. The phenomenon has found numerous applications in physics, neuroscience, biology, medicine, mechanics and other fields. The present paper concerns this phenomenon for parametrically excited stochastic systems, i.e. systems that feature deterministic input signals that affect their parameters, e.g. stiffness, damping or mass properties. Parametrically excited systems are now widely used for signal sensing, filtering and amplification, particularly in micro- and nanoscale applications. And noise and uncertainty can be essential for systems at this scale. Thus, these systems potentially can exhibit stochastic resonance. In the present paper, we use a “deterministic” approach to describe the stochastic resonance phenomenon that implies replacing noise by deterministic high-frequency excitations. By means of the approach, we show that stochastic resonance can occur for parametrically excited systems and determine the corresponding resonance conditions.

Keywords

Stochastic resonanceparametric excitationhigh-frequency vibrationeffective propertiesoscillatory strobodynamics

MSC classification

Primary: 34F15: Resonance phenomena
Secondary: 60H10: Stochastic ordinary differential equations 34K50: Stochastic functional-differential equations
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Special Issue 5: Stochastic Analysis in Applications , October 2019 , pp. 986 - 1003
Copyright
© Cambridge University Press 2018 

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Footnotes

†

The work is carried out with financial support from the Russian Science Foundation, Grant 17-79-30056 (project “REC Mekhanobr-Tekhnika”).

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