Stochastic multiresonance and correlation-time-controlled stability for a harmonic oscillator with fluctuating frequency.

The long-time behavior of the first two moments and the correlation function for the output signal of a harmonic oscillator with fluctuating frequency subjected to an external periodic force and an additive thermal noise is considered analytically. The colored fluctuations of the oscillator frequency are modeled as a three-level Markovian noise. Using the Shapiro-Loginov formula, the exact expressions of several stochastic resonance (SR) characteristics such as the spectral amplification, the variance of the output signal, the signal-to-noise ratio, and the SR gain have been calculated. The nonmonotonic dependence of the SR characteristics versus the noise parameters as well as versus the input signal frequency and also the conditions for the appearance of energetic instability are analyzed. In particular, the multiresonancelike behavior of the variance and the signal-to-noise ratio as functions of the noise correlation time are observed and the connection between the occurrence of energetic instability and the phenomenon of stochastic multiresonance is established. Some unexpected effects such as the hypersensitive response of the spectral amplification to small variations of the noise amplitude encountered in the case of a large flatness of the colored noise are also discussed.