Stochastic resonance in a fractional oscillator with random mass and random frequency. (English) Zbl 1360.82069
Summary: For a fractional linear oscillator subjected to two multiplicative dichotomous noises and a additive fractional Gaussian noise and driven by a periodic signal, we study the stochastic resonance (SR) in this paper. Using (fractional) Shapiro-Loginov formula and the Laplace transformation technique, we acquire the exact expression of the first-order moment of the system’s steady response. Meanwhile, we discuss the evolutions of the output amplitude with frequency of the periodic signal, noise parameters, fractional order, and friction coefficient. We find that SR in the wide sense existing in this system. Specially, the evolution of the output amplitude with frequency of the periodic signal presents one-peak oscillation and two-peak oscillation. Moreover, the friction coefficient can induce stochastic multi-resonance.
MSC:
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
| 44A10 | Laplace transform |
| 60H25 | Random operators and equations (aspects of stochastic analysis) |
Keywords:
stochastic resonance in the wide sense; fractional oscillator; dichotomous; noise; random mass; random frequencyReferences:
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