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Nonlinear Dynamics

, Volume 93, Issue 2, pp 767–778 | Cite as

On a “deterministic” explanation of the stochastic resonance phenomenon

  • I. I. Blekhman
  • V. S. Sorokin
Original Paper

Abstract

The present paper concerns the analysis of the stochastic resonance phenomenon that previously has been thoroughly studied and found numerous applications in physics, neuroscience, biology, medicine, mechanics, etc. A novel “deterministic” explanation of this phenomenon is proposed that allows broadening the range of dynamical systems for which the phenomenon can be predicted and analysed. Our results indicate that stochastic resonance, similarly to vibrational resonance, arises due to deterministic reasons: it occurs when a system is excited with two (or more) vastly different frequencies, one of which is much higher than another. The effective properties of the system, e.g. stiffness or mass, change under the action of the high-frequency excitation; and the low-frequency excitation acts on this “modified” system leading to low-frequency resonances. In the case of a broadband random excitation, the high-frequency part of the excitation spectrum affects the effective properties of the system. The low-frequency part of the spectrum acts on this modified system. Thus by varying the noise intensity one can change properties of the system and attain resonances. This explanation allows using “deterministic” approach, i.e. replacing noise by high-frequency excitation, when studying the stochastic resonance phenomenon. Employing this approach, we demonstrate that linear and nonlinear stochastic systems with varying parameters, i.e. parametrically excited systems, can exhibit the phenomenon and determine the corresponding resonance conditions.

Keywords

Stochastic resonance Deterministic explanation High-frequency excitation Effective properties Oscillatory strobodynamics Parametric excitation 

Notes

Acknowledgements

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

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mekhanobr-Tekhnika Research and Engineering Corp.St. PetersburgRussia
  2. 2.Institute of Problems in Mechanical Engineering RASSt. PetersburgRussia
  3. 3.Department of Mechanical EngineeringThe University of AucklandAucklandNew Zealand

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