  We analyze several aspects of the phenomenon of stochastic resonance in
reaction-diffusion systems, exploiting the nonequilibrium potential's
framework. The generalization of this formalism (sketched in the appendix) to
extended systems is first carried out in the context of a simplified scalar
model, for which stationary patterns can be found analytically. We first show
how system-size stochastic resonance arises naturally in this framework, and
then how the phenomenon of array-enhanced stochastic resonance can be further
enhanced by letting the diffusion coefficient depend on the field. A yet less
trivial generalization is exemplified by a stylized version of the
FitzHugh-Nagumo system, a paradigm of the activator-inhibitor class. After
discussing for this system the second aspect enumerated above, we derive from
it -through an adiabatic-like elimination of the inhibitor field- an effective
scalar model that includes a nonlocal contribution. Studying the role played by
the range of the nonlocal kernel and its effect on stochastic resonance, we
find an optimal range that maximizes the system's response.
