Stochastic resonance in noisy maps as dynamical threshold-crossing systems

Interplay of noise and periodic modulation of system parameters for the log istic map in the region after the first bifurcation and for the kicked spin model with Ising anisotropy and damping is considered. Fur both maps two d istinct symmetric states are present that correspond to different phases of the period-2 orbit of the logistic map and to disjoint attractors of the s pin map. The periodic force modulates the transition probabilities From any state to the opposite one symmetrically. It follows that the maps behave a s threshold-crossing systems with internal dynamics, and stochastic resonan ce (maximum of die signal-to-noise ratio in thr: signal reflecting the occu rrence of jumps between the symmetric states) in both models is observed. N umerical simulations agree qualitatively with analytic results based on the adiabatic theory.