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| Stochastic resonance has been the object of extensive research in the last decades. The
term describes a phenomenon in nonlinear systems where a weak signal can be be amplified and optimized by the presence of noise. This rather counter-intuitive effect was first presented in works by R.~Benzi and collaborators to address the problem of periodically recurrent ice ages.
A standard model for SR is given by a damped particle in a periodically oscillating double-well potential with white noise: if the periodic forcing is too weak for the particle to move periodically between wells, noise-induced hopping synchronized with the forcing can nevertheless be observed for optimal values of the parameters. The phenomenon is relevant in a number of fields such as signal analysis, biology, neurosciences and climate studies.
Though widely studied in statistical physics and the different fields of application, and despite showing the characters of a "bifurcation", there are few theoretical results on the dynamical systems underlying the phenomenon, in particular in term of bifurcation theory. Starting from results by H.~Crauel and F.~Flandoli and by J.~Lamb, M.~Rasmussen and collaborators, we studied the SR in the framework of bifurcation theory for random dynamical systems. |
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