  An amenable, analytical two-state description of the nonlinear population
dynamics of a noisy bistable system driven by a rectangular subthreshold signal
is put forward. Explicit expressions for the driven population dynamics, the
correlation function (its coherent and incoherent part), the signal-to-noise
ratio (SNR) and the Stochastic Resonance (SR) gain are obtained. Within a
suitably chosen range of parameter values this reduced description yields
anomalous SR-gains exceeding unity and, simultaneously, gives rise to a
non-monotonic behavior of the SNR vs. the noise strength. The analytical
results agree well with those obtained from numerical solutions of the Langevin
equation.
