Friction-induced Resonance in a Noisy Fractional Oscillator

The influence of the friction coefficient on the long-time behavior of the spectral amplification, variance, and signal-to-noise ratio (SNR) found for the output signal of a fractional oscillator with fluctuating eigenfrequency subjected to a periodic force is considered. The influence of the fluctuating environment is modeled by a multiplicative white noise and by an additive noise with a zero mean. The viscoelastic friction kernel with memory is assumed as a power-law function of time. The study is a follow-up of a previous investigation of a noisy fractional oscillator [Phys. Rev. E 81, 041122 (2010)]. On the basis of exact formulas it is demonstrated that an interplay of multiplicative noise and memory can generate a multiresonance of SNR versus the friction coefficient. The necessary and sufficient conditions for such a resonance effect are also discussed. Particularly, it is shown that resonance-like behavior of SNR versus the friction coefficient is qualitatively different in the cases of external and internal additive noises.