Abstract：Aiming at the problem of singularity in the study of stochastic resonance based on commonly used fractional calculus, a research method of stochastic resonance in bistable systems based on Atangana-Baleanu fractional calculus is proposed. First, according to the definition of Atangana-Baleanu fractional calculus, the Langevin equation is constructed to describe the stochastic resonance system. Second, it is approximated by the improved Oustaloup algorithm. Finally, simulation program is written to study the effect of parameter changes on stochastic resonance using the single variable control method. The simulation results show that when the noise intensity is constant, by changing the fractional order derivative order, there is a nonlinear relation between the order of fractional derivative and the power spectrum of the output signal and there is an optimal order of fractional derivative to generate stochastic resonance. When the order of fractional derivative is constant, by changing the noise intensity, there is a nonlinear relation between the noise intensity and the power spectrum value of the output signal and there is an optimal noise intensity to generate stochastic resonance.
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2021, Vol. 42 
