Characterization of stochastic resonance

Traditional quantities used to characterize stochastic resonance possess the common feature of low sensitivity to noise variation in the sense that they vary slowly about the optimal noise level. In potential applications of stochastic resonance such as device development, a high sensitivity to noise may be required. Here we show that, when the resonance is understood as a manifestation of phase synchronization, the average synchronization time between the input and output signal has an extremely high sensitivity in that it exhibits a cusp-like behavior about the optimal noise level. Theoretical analysis and numerical evidence are provided to establish the cusp-like behavior and its generality.