Stochastic Resonance
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A01=Dierk Peithmann
A01=Ilya Pavlyukevich
A01=Peter Imkeller
A01=Samuel Herrmann
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Author_Dierk Peithmann
Author_Ilya Pavlyukevich
Author_Peter Imkeller
Author_Samuel Herrmann
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Product details
- ISBN 9781470410490
- Weight: 525g
- Dimensions: 178 x 254mm
- Publication Date: 30 Apr 2014
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Hardback
- Language: English
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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 optimising 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.
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 optimising 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.
Samuel Herrmann, Université de Bourgogne, Dijon, France
Peter Imkeller, Humboldt-Universität zu Berlin, Germany
Ilya Pavlyukevich, Friedrich-Schiller-Universität Jena, Germany
Dierk Peithmann, Essen, Germany
Peter Imkeller, Humboldt-Universität zu Berlin, Germany
Ilya Pavlyukevich, Friedrich-Schiller-Universität Jena, Germany
Dierk Peithmann, Essen, Germany
