Abstract
Stochastic resonance (SR) is a prominent phenomenon in many natural and engineered noisy systems, whereby the response to a periodic forcing is greatly amplified when the intensity of the noise is tuned to within a specific range of values. We propose here a general mathematical framework based on large deviation theory and, specifically, on the theory of quasipotentials, for describing SR in noisy N-dimensional nonequilibrium systems possessing two metastable states and undergoing a periodically modulated forcing. The drift and the volatility fields of the equations of motion can be fairly general, and the competing attractors of the deterministic dynamics and the edge state living on the basin boundary can, in principle, feature chaotic dynamics. Similarly, the perturbation field of the forcing can be fairly general. Our approach is able to recover as special cases the classical results previously presented in the literature for systems obeying detailed balance and allows for expressing the parameters describing SR and the statistics of residence times in the two-state approximation in terms of the unperturbed drift field, the volatility field, and the perturbation field. We clarify which specific properties of the forcing are relevant for amplifying or suppressing SR in a system and classify forcings according to classes of equivalence. Our results indicate a route for a detailed understanding of SR in rather general systems.
Highlights
Stochastic resonance (SR) is a rather special and somewhat counterintuitive mechanism where noise plays the constructive role of catalyzing the amplification of the response of a system to a weak periodic signal
The resonance condition we find agrees, obviously, with the result presented in Ref. [19]; the main improvement we get in our result is that we can relate all parameters in the previous equation to the unperturbed equations of motion via
Our findings give as a special case the classical results valid for systems obeying a detailed balance, as in the case of N-dimensional gradient flows forced by standard additive noise
Summary
Stochastic resonance (SR) is a rather special and somewhat counterintuitive mechanism where noise plays the constructive role of catalyzing the amplification of the response of a system to a weak periodic signal. The problem has been later generalized to the case of more general noise laws [32,33,34,35], while a general treatment of SR in an asymmetric potential with complex stochastic forcing has been presented by Qiao et al [36]. [19,37], while general results have been presented for the asymmetric case and for non-Gaussian stochastic forcing in Refs. Most of the results on SR have been derived in the case of one-dimensional systems or, more generally, of Ndimensional gradient flows. Our treatment will in principle include the case of stochastically perturbed systems featuring, when noise is removed, two competing chaotic attractors supported on strange sets. Note that different mechanisms of SR-like phenomena for chaotic systems have been discussed in the literature, where deterministic chaos plays the role of internally generated noise, and no external stochastic forcing is needed. The Appendix contains results pertaining to the statistics of residence times, i.e., the time intervals spent consecutively in each state before a noise-induced transition takes place
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