Quantitative measures of stochastic resonance effect based on switch-phase distribution

Stochastic resonance (SR) effect observed in biological, physical, and engineering systems is commonly described quantitatively by power spectral measures that require complex mathematical operations and long, continuous observation. Here, we propose two measures based on the switch-phase distribution to qualitatively describe the SR effect, namely, the power norm and the probability that the switch phase lies within a specific range around the peak of the switch-phase distribution. They are easy to be practically determined from a single long run or from multiple short runs. Further, theses metrics were used to quantitatively describe the SR effect observed experimentally in Chua's circuit, operating in chaotic single-scroll regime, forced by 1 kHz sinusoidal subthreshold internal electric or external magnetic signal with switches between attractors induced by internal electric Gaussian noise. The dependence of the switch-phase distributions on the noise intensity for two types of oriented switches are presented. The proposed measures give the optimal noise level as obtained with the widely used signal-to-noise ratio (SNR) measure. The dependence of the first measure on the noise intensity is the same as the SNR dependence. The second measure decreases with increasing noise intensity and has an inflection point at the optimal noise intensity, being almost linear in the vicinity of this point. This dependence on the noise intensity hints for many potential applications, e.g., to aperiodic signal coding and decoding. Both measures are particularly useful for adaptive stochastic resonance and parallel processing.