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Stochastic resonance: a mathematical approach in the small noise limit

Stochastic resonance is a phenomenon arising in a wide spectrum of areas in the sciences ranging from physics through neuroscience to chemistry and biology. This book presents a mathematical approach to stochastic resonance which is based on a large deviations principle (LDP) for randomly perturbed...

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Detalles Bibliográficos
Autores principales: Herrmann, Samuel, Imkeller, Peter, Pavlyukevich, Ilya, Peithmann, Dierk
Lenguaje:eng
Publicado: American Mathematical Society 2013
Materias:
Acceso en línea:http://cds.cern.ch/record/2623040
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author Herrmann, Samuel
Imkeller, Peter
Pavlyukevich, Ilya
Peithmann, Dierk
author_facet Herrmann, Samuel
Imkeller, Peter
Pavlyukevich, Ilya
Peithmann, Dierk
author_sort Herrmann, Samuel
collection CERN
description Stochastic resonance is a phenomenon arising in a wide spectrum of areas in the sciences ranging from physics through neuroscience to chemistry and biology. This book presents a mathematical approach to stochastic resonance which is based on a large deviations principle (LDP) for randomly perturbed dynamical systems with a weak inhomogeneity given by an exogenous periodicity of small frequency. Resonance, the optimal tuning between period length and noise amplitude, is explained by optimizing the LDP's rate function. The authors show that not all physical measures of tuning quality are robust with respect to dimension reduction. They propose measures of tuning quality based on exponential transition rates explained by large deviations techniques and show that these measures are robust. The book sheds some light on the shortcomings and strengths of different concepts used in the theory and applications of stochastic resonance without attempting to give a comprehensive overview of the many facets of stochastic resonance in the various areas of sciences. It is intended for researchers and graduate students in mathematics and the sciences interested in stochastic dynamics who wish to understand the conceptual background of stochastic resonance.
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spelling cern-26230402021-04-21T18:47:51Zhttp://cds.cern.ch/record/2623040engHerrmann, SamuelImkeller, PeterPavlyukevich, IlyaPeithmann, DierkStochastic resonance: a mathematical approach in the small noise limitMathematical Physics and MathematicsStochastic resonance is a phenomenon arising in a wide spectrum of areas in the sciences ranging from physics through neuroscience to chemistry and biology. This book presents a mathematical approach to stochastic resonance which is based on a large deviations principle (LDP) for randomly perturbed dynamical systems with a weak inhomogeneity given by an exogenous periodicity of small frequency. Resonance, the optimal tuning between period length and noise amplitude, is explained by optimizing the LDP's rate function. The authors show that not all physical measures of tuning quality are robust with respect to dimension reduction. They propose measures of tuning quality based on exponential transition rates explained by large deviations techniques and show that these measures are robust. The book sheds some light on the shortcomings and strengths of different concepts used in the theory and applications of stochastic resonance without attempting to give a comprehensive overview of the many facets of stochastic resonance in the various areas of sciences. It is intended for researchers and graduate students in mathematics and the sciences interested in stochastic dynamics who wish to understand the conceptual background of stochastic resonance.American Mathematical Societyoai:cds.cern.ch:26230402013
spellingShingle Mathematical Physics and Mathematics
Herrmann, Samuel
Imkeller, Peter
Pavlyukevich, Ilya
Peithmann, Dierk
Stochastic resonance: a mathematical approach in the small noise limit
title Stochastic resonance: a mathematical approach in the small noise limit
title_full Stochastic resonance: a mathematical approach in the small noise limit
title_fullStr Stochastic resonance: a mathematical approach in the small noise limit
title_full_unstemmed Stochastic resonance: a mathematical approach in the small noise limit
title_short Stochastic resonance: a mathematical approach in the small noise limit
title_sort stochastic resonance: a mathematical approach in the small noise limit
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2623040
work_keys_str_mv AT herrmannsamuel stochasticresonanceamathematicalapproachinthesmallnoiselimit
AT imkellerpeter stochasticresonanceamathematicalapproachinthesmallnoiselimit
AT pavlyukevichilya stochasticresonanceamathematicalapproachinthesmallnoiselimit
AT peithmanndierk stochasticresonanceamathematicalapproachinthesmallnoiselimit