Stochastic resonance in a fractional linear oscillator subject to random viscous damping and signal-modulated noise

• We investigate the stochastic resonance in a fractional linear system with random viscous damping subject to dichotomous noise and signal-modulated noise.
• The output-amplitude-gain (OAG) is a non-monotonic function of the viscous damping of the oscillator.
• The OAG is a non-monotonic function of the correlation rate of the dichotomous noise.
• The OAG varies non-monotonically with the friction coefficient.

The stochastic resonance in a fractional linear system with random viscous damping driven by a dichotomous noise and signal-modulated noise is investigated. By the use of the properties of the noises and the Shapiro-Loginov formula and Laplace transform technology, the exact expression for the mean output-amplitude-gain (OAG) of the system is obtained. The non-monotonic influence of the viscous damping of the oscillator on the OAG is found. It is shown that the OAG is a non-monotonic function of the intensity and the correlation rate of the dichotomous noise. The OAG varies non-monotonically with the friction coefficient, with the frequency of the driving signal, with the frequency of the linear oscillator, as well as with the fractional exponent of the fractional oscillator.