  Stochastic resonance (SR) is a prominent phenomenon in many natural and
engineered noisy system, 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 quasi-potentials, for
describing SR in noisy N-dimensional non-equilibrium 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.
