
Preface  Introduction  Preview Material  Table of Contents  Supplementary Material 
Mathematical Surveys and Monographs 2014; 189 pp; hardcover Volume: 194 ISBN10: 1470410494 ISBN13: 9781470410490 List Price: US$77 Member Price: US$61.60 Order Code: SURV/194 See also: Large Deviations for Stochastic Processes  Jin Feng and Thomas G Kurtz Nonautonomous Dynamical Systems  Peter E Kloeden and Martin Rasmussen Large Deviations  JeanDominique Deuschel and Daniel W Stroock  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. Readership Graduate students and research mathematicians interested in large deviations and stochastic resonance. 


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