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 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.