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Theory of stochastic resonance
Abstract
The concept of stochastic resonance has been introduced previously to describe a curious phenomenon in bistable systems subject to both periodic and random forcing: an increase in the input noise can result in an improvement in the output signal-to-noise ratio. In this paper we present a detailed theoretical and numerical study of stochastic resonance, based on a rate equation approach. The main result is an equation for the output signal-to-noise ratio as a function of the rate at which noise induces hopping between the two states. The manner in which the input noise strength determines this hopping rate depends on the precise nature of the bistable system. For this reason, the theory is applied to two classes of bistable systems, the double-well (continuous) system and the two-state (discrete) system. The theory is tested in detail against digital simulations.
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Cites
On the use of windows for harmonic analysis with the discrete Fourier transform
Harris, F. J. (1978) · Proceedings of the IEEE · doi:10.1109/proc.1978.10837 · Cited by 7,326
Cited by
Gammaitoni, L., Hänggi, P., Jung, P., & Marchesoni, F. (1998) · Reviews of Modern Physics · doi:10.1103/revmodphys.70.223 · Cited by 5,443
Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs
Wiesenfeld, K., & Moss, F. (1995) · Nature · doi:10.1038/373033a0 · Cited by 1,830
Self-citationEmerging concepts for the dynamical organization of resting-state activity in the brain
Deco, G., Jirsa, V. K., & McIntosh, A. R. (2011) · Nature reviews. Neuroscience · doi:10.1038/nrn2961 · Cited by 1,798
What Is Stochastic Resonance? Definitions, Misconceptions, Debates, and Its Relevance to Biology
McDonnell, M. D., & Abbott, D. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000348 · Cited by 774
Periodically driven stochastic systems
Jung, P. (1993) · Physics Reports · doi:10.1016/0370-1573(93)90022-6 · Cited by 473
Metadata
- Authors
- McNamara, B., & Wiesenfeld, K.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1989-05-01
- Volume
- 39
- Issue
- 9
- Pages
- 4854-4869
- ISSN
- 0556-2791 (ISSN-L)
- OpenAlex
- W2068501389
- Cited by
- 1,559
- References
- 1
- FWCI
- 16.29
- Type
- journal article
- Language
- en
- Open access
- closed
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- McNamara, B., & Wiesenfeld, K. (1989). Theory of stochastic resonance. Physical Review A. https://doi.org/10.1103/physreva.39.4854
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