  The occurrence of stochastic resonance in bistable systems undergoing
anomalous diffusions, which arise from density-dependent fluctuations, is
investigated with emphasis on the analytical formulation of the problem as well
as a possible analytical derivation of key quantifiers of stochastic resonance.
The nonlinear Fokker-Planck equation describing the system dynamics, together
with the corresponding Ito-Langevin equation, are formulated. In the
linear-response regime analytical expressions of the spectral amplification, of
the signal-to-noise ratio and of the hysteresis loop area are derived as
quantifiers of stochastic resonance. These quantifiers are found to be strongly
dependent on the parameters controlling the type of diffusion, in particular
the peak characterizing the signal-to-noise ratio occurs only in close ranges
of parameters. Results introduce the relevant information that taking into
consideration the interactions of anomalous diffusive systems with a periodic
signal, can provide a better understanding of the physics of stochastic
resonance in bistable systems driven by periodic forces.
