M. Qian et al., Stochastic resonance on a circle without excitation: Physical investigation and peak frequency formula, PHYS REV E, 62(5), 2000, pp. 6469-6474
In this article the existence of stochastic resonance (SR) without external
force in a simplified circular system for different values of the control
parameter b is considered. The average power spectra are calculated as well
as the signal-to-noise ratio as a measure for stochastic resonance. It is
shown that in the monostable and semistable (b<1 and b=1) cases coherent os
cillations occur and SR exists. For the case b>1, the system is oscillatory
and noise plays only a destructive role; therefore no SR occurs. The rotat
ion number of the system is calculated and compared to the peak frequency o
f the power spectrum. Although the coincidence in the noisy case is not as
good as that in the deterministic case, we can derive an empirical formula
between the peak frequency of the power spectrum and the rotation number of
the system, which is in good agreement with results of numerical simulatio
ns.