Effect of recycled noise of a fractional nonlinear oscillator subjected to multiplicative and additive recycled noises

The stochastic resonance (SR) phenomenon of a fractional nonlinear oscillator with multiplicative noise and additive recycled noise is investigated. The transition rates caused by the master noise and by the recycled noise have been deduced based on the two-state theory. The spectral amplification (SA) of the oscillator has been derived by applying linear response theory. It is shown that the periodic SR phenomenon occurs when the SA varies with the time delay of the recycled noise. A single resonance peak takes place when the SA changes with the increase in the feedback intensity of the recycled noise. The SA presents a resonance peak at a certain amount of multiplicative and additive noise. Damping-induced SR appears when the SA changes with the damping coefficient of the oscillator.