Stochastic resonance for a fractional linear oscillator with two-kinds of fractional-order derivatives subject to multiplicative and signal-modulated noise

The stochastic resonance phenomenon for a fractional linear oscillator with two-kinds of fractional-order derivatives driven by multiplicative noise and signal-modulated noise is investigated. Based on linear system theory, applying the characteristics of the Gamma function and the definition of the fractional-order derivative, the output-amplitude-gain (OAG) for the oscillator is derived. The analysis results show that the OAG is a non-monotonic function of the exponents of the fractional-order derivatives, the effect of the two exponents on the OAG is different. The OAG varies non-monotonically with a variation of the system driving frequency. The OAG behaves non-monotonically with an increase of the two friction coefficients of the fractional oscillator. The nonlinear dependence of the system frequency and the correlation rate of the multiplicative noise are analyzed.